HLSM-BlackScholes-American.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# How to Price and Hedge American Options Using Regression-based Methods\n",
    "\n",
    "## Hedged Least Square Method\n",
    "\n",
    "Author: Jerry Xia\n",
    "\n",
    "Date: 2018/08/27"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Introduction\n",
    "\n",
    "This is a Python Notebook about an inovative method of the Monte Carlo simulation, Hedged Least Square Method (HLSM) in order to price and hedge American type options. In this script, I implemented the following variance reduction methods as well as their antithetic variates' version:\n",
    "\n",
    "* regular Monte Carlo for European options\n",
    "* least square Monte Carlo for American options\n",
    "* Monte Carlo with delta-based control variates for European options\n",
    "* optimal hedged Monte Carlo for European options\n",
    "* hedged least square Monte Carlo for American options\n",
    "\n",
    "Due to the significant efficience and robustness, I mainly focus on the optimal hedged least square Monte Carlo (OHLSMC) in option pricing. We invoke this method to price American options and make comparison with the original least square monte carlo (LSM).\n",
    "\n",
    "### 1.1 Facts\n",
    "* The option price is not simply the average value of the discounted future pay-off over the objective (or historical) probability distribution\n",
    "* The requirement of absence of arbitrage opportunities is equivalent to the existence of \"risk-neutral measure\", such that the price is indeed its average discounted future pay-off.\n",
    "* Risk in option trading cannot be eliminated\n",
    "\n",
    "### 1.2 Objective\n",
    "* It would be satisfactory to have an option theory where the objective stochastic process of the underlying is used to calculate the option price, the hedge strategy and the *residual risk*.\n",
    "\n",
    "### 1.3 Advantages\n",
    "* It is a versatile methods to price complicated path-dependent options.\n",
    "* Considerable variance reduction scheme for Monte Carlo\n",
    "* It provide not only a numerical estimate of the option price, but also of the optimal hedge strategy and of the residual risk.\n",
    "* This method does not rely on the notion of risk-neutral measure, and can be used to any model of the true dynamics of the underlying"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## 2 Underlying dynamics\n",
    "\n",
    "### Black-Scholes Model\n",
    "$$dS = \\mu S dt + \\sigma S dW_t$$\n",
    "$$log S_{t+1} = log S_t +(\\mu - \\frac{\\sigma^2}{2})\\Delta t + \\sigma \\sqrt{\\Delta t} \\epsilon$$\n",
    "where\n",
    "$$\\epsilon \\sim N(0,1)$$\n",
    "In risk neutral measure, $\\mu = r - q$. \n",
    "### Heston Model\n",
    "The basic Heston model assumes that $S_t$, the price of the asset, is determined by a stochastic process:\n",
    "$$\n",
    "dS_t = \\mu S_t dt + \\sqrt{v_t} S_t d W_t^S\\\\\n",
    "dv_t = \\kappa (\\theta - v_t) dt + \\xi \\sqrt{v_t} d W_t^v\n",
    "$$\n",
    "where \n",
    "$$E[dW_t^S,dW_t^v]=\\rho dt$$\n",
    "In risk neutral measure, $\\mu = r - q$. "
   ]
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   "source": [
    "## 3 Methodology\n",
    "\n",
    "### 3.1 Notations\n",
    "Option price always requires to work backward. That is because the option price is known exactly at the maturity. As with other schemes, we determine the option price step by step from the maturity $t=K\\tau=T$ to the present time $t=0$. The unit of time being $\\tau$, for example, one day. We simulate $N$ trajectories. In trajectory i, the price of the underlying asset at time $k\\tau$ is denoted as $S_k^{(i)}$. The price of the derivative at time $k\\tau$ is denoted as $C_k$, and the hedge function is $H_k$. We define an optimal hedged portfolio as\n",
    "$$W_k^{(i)} = C_k(S_k^{(i)}) + H_k(S_k^{(i)})S_k^{(i)}$$\n",
    "The one-step change of our portfolio is\n",
    "$$\\Delta W_k^{(i)}= df(k,k+1) C_{k+1}(S_{k+1}^{(i)}) - C_k(S_k^{(i)}) + H_k(S_{k}^{(i)}) (df2(k,k+1) S_{k+1}^{(i)} - S_{k}^{(i)})$$\n",
    "Where $df(k,k+1)$ is the discounted factor from time $k\\tau$ to $(k+1) \\tau$, $df2(k,k+1)$ is the discounted factor considering dividend $e^{-(r-q)(t_{k+1}-t_k)}$\n",
    "\n",
    "### 3.2 Objective\n",
    "The optimal hedged algorithm can be interpreted as the following optimal problem\n",
    "\n",
    "\\begin{align}\n",
    "\\mbox{minimize}\\quad & \\quad Var[\\Delta W_k]\\\\\n",
    "\\mbox{subject to}\\quad & \\quad E[\\Delta W_k]=0\n",
    "\\end{align}\n",
    "\n",
    "It means we should try to minimize the realized volatility of hedged portfolio while maintaining the expected value of portfolio unchanged.\n",
    "\n",
    "### 3.3 Basis Functions\n",
    "The original optimization is very difficult to solve. Thus we assume a set of basis function and solved it in such subspace. We use $N_C$and $N_H$ to denote the number of basis functions for price and hedge.\n",
    "\n",
    "\\begin{align}\n",
    "C_k(\\cdot) &= \\sum_{i=0}^{N_C} a_{k,i} A_i(\\cdot)\\\\\n",
    "H_k(\\cdot) &= \\sum_{i=0}^{N_H} b_{k,i} B_i(\\cdot)\n",
    "\\end{align}\n",
    "\n",
    "The basis functions $A_i$ and $B_i$ are priori determined and need not to be identical. The coefficients $a_i$ and $b_i$ can be calibrated by solving the optimal problem.\n",
    "\n",
    "### 3.4 Numerical Solution\n",
    "\n",
    "\\begin{align}\n",
    "\\mbox{minimize}\\quad & \\quad \\frac{1}{N} \\sum_{i=1}^N \\Delta W_k^{(i)2}\\\\\n",
    "\\mbox{subject to}\\quad & \\quad \\frac{1}{N} \\sum_{i=1}^N \\Delta W_k^{(i)}=0\n",
    "\\end{align}\n",
    "\n",
    "Denote the discounted forward underlying price change at time $k\\tau$ as\n",
    "\n",
    "$$\\Delta S_k = df2(k,k+1) S_{k+1} - S_k$$\n",
    "\n",
    "Define\n",
    "\n",
    "\\begin{align}\n",
    "Q_k &= \\begin{bmatrix}\n",
    "    -A_{k,1}(S_k^{(1)}) & \\cdots & -A_{k,N_C}(S_k^{(1)}) & B_{k,1}(S_k^{(1)})\\Delta S_k^{(1)}& \\cdots  & B_{k,N_H}(S_k^{(1)})\\Delta S_k^{(1)} \\\\\n",
    "    -A_{k,1}(S_k^{(2)}) & \\cdots & -A_{k,N_C}(S_k^{(2)}) & B_{k,1}(S_k^{(2)})\\Delta S_k^{(2)}& \\cdots  & B_{k,N_H}(S_k^{(1)})\\Delta S_k^{(2)} \\\\\n",
    "    \\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\\n",
    "    -A_{k,1}(S_k^{(N)}) & \\cdots & -A_{k,N_C}(S_k^{(N)}) & B_{k,1}(S_k^{(N)})\\Delta S_k^{(N)}& \\cdots  & B_{k,N_H}(S_k^{(N)})\\Delta S_k^{(N)}\n",
    "    \\end{bmatrix}\\\\\\\\\n",
    "c_k &= (a_{k,1}, \\cdots a_{k,N_C}, b_{k,1}, \\cdots, b_{k,N_H})^T\\\\\\\\\n",
    "v_{k} &= df(k,k+1) C_{k+1}(S_{k+1}^{})\n",
    "\\end{align}\n",
    "\n",
    "As for $v_k$, note that we know the exact value at maturity, which means there is no need to approximate price in terms of basis functions, that is\n",
    "\n",
    "\\begin{align}\n",
    "v_k = \\begin{cases}\n",
    "df(N-1,N)\\ payoff(S_N),\\quad & k=N-1\\\\\n",
    "df(k,k+1)\\ \\sum_{i=1}^{N_C} a_{k+1,i} A_i(S_{k+1}), \\quad & 0<k<N-1\\\\\n",
    "df(0,1)\\ C_1(S_1), \\quad & k=0\n",
    "\\end{cases}\n",
    "\\end{align}\n",
    "\n",
    "Then, the optimization problem can be expressed as\n",
    "\n",
    "\\begin{align}\n",
    "\\arg\\min_{c_k}\\quad & \\quad (v_{k} + Q_k c_k)^T (v_{k} + Q_k c_k)\\\\\n",
    "\\mbox{subject to}\\quad & \\quad 1_{[N\\times1]}^T (v_{k}  + Q_k c_k)=0\n",
    "\\end{align}\n",
    "\n",
    "In step k, since we already know the information ($v_{k}$) in step k+1. By canceling the constant term, the optimal problem can be simplified as the following \n",
    "\n",
    "\\begin{align}\n",
    "\\arg\\min_{c_k}\\quad & \\quad 2 v_{k}^T Q_k c_k + c_k^T Q_k^T Q_k c_k\\\\\n",
    "\\mbox{subject to}\\quad & \\quad 1_{[N\\times1]}^T v_{k}  + 1_{[N\\times1]}^T Q_k c_k=0\n",
    "\\end{align}"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.5 Convex Optimization Problem\n",
    "\n",
    "Let us first review the standard form of linear constrained quadratic programming problem:\n",
    "\n",
    "\\begin{align}\n",
    "    \\min_{x} \\quad & \\frac{1}{2} x^T P x + q^T x\\\\\n",
    "    \\mbox{subject to} \\quad &G x \\preceq h\\\\\n",
    "    &A x = b\n",
    "\\end{align}\n",
    "\n",
    "Note that $x^T$ means the transpose of vector x, and $G x \\preceq h$denotes the inequality is taken element-wise over the vectors $G x$ and $h$. The objective function is convex if and only if the matrix $P$ is positive-semidefinite(Hermitian matrix all of whose eigenvalues are nonnegative), which is the realm we concern with.\n",
    "\n",
    "Recall that the constrained optimization problem:\n",
    "\n",
    "\\begin{align}\n",
    "\\arg\\min_{c_k}\\quad & \\quad  v_{k}^T Q_k c_k + \\frac{1}{2}c_k^T Q_k^T Q_k c_k\\\\\n",
    "\\mbox{subject to}\\quad & \\quad 1_{[N\\times1]}^T v_{k}  + 1_{[N\\times1]}^T Q_k c_k=0\n",
    "\\end{align}\n",
    "\n",
    "Correspondingly, we make the connection by letting\n",
    "\n",
    "\\begin{align}\n",
    "    x &= c_k\\\\\n",
    "    P &= Q_k^T Q_k\\\\\n",
    "    q &= Q_k^T v_k\\\\\n",
    "    A &= 1_{[N\\times1]}^T Q_k\\\\\n",
    "    b &= -1_{[N\\times1]}^T v_{k}\n",
    "\\end{align}\n",
    "\n",
    "The hard work is almost over right now. As you would always find, formulating the problem is usually the hard step. Invoking a solver is straightforward.\n",
    "\n",
    "Note that when $k=0$, the degree of freedom of the quadratic problem decreases to 2. Because here the only concerns are price and hedge at time zero (we don't need to project them into a high dimension space). Let $x=[C_0, H_0]^T$\n",
    "\n",
    "\\begin{align}\n",
    "    Q_0 &= \\begin{bmatrix}\n",
    "    -1 & \\Delta S_0^{(1)}\\\\\n",
    "    \\vdots & \\vdots\\\\\n",
    "    -1 & \\Delta S_0^{(N)}\n",
    "    \\end{bmatrix}\\\\\n",
    "    P &= Q_0^T Q_0\\\\\n",
    "    q &= Q_0^T v_0\\\\\n",
    "    A &= 1_{[N \\times 1]}^T Q_0\\\\\n",
    "    b &= -1_{[N \\times 1]}^T v_0\n",
    "\\end{align}"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 Variance reduction and other methods\n",
    "The rate of convergence of the Monte Carlo simulation is $O\\left(\\max \\left( \\Delta t, \\frac{1}{N_x} \\right)\\right)$. The variance reduction techniques are used to reduce the constant factor corresponding to the Monte Carlo approximation $O \\left(\\frac{1}{N_x}\\right)$. Some of the most used variance reduction techniques are:\n",
    "\n",
    "* Control Variates\n",
    "* Antithetic Variates\n",
    "* Moment Matching\n",
    "\n",
    "In this part we selected antithetic variates and delta-based control variates methods as a supplement to optimal hedged monte carlo simulation.\n",
    "\n",
    "### 4.1 Antithetic variates\n",
    "The main idea of this technique is to look at the asset equation that you aretrying to simulate:\n",
    "$$d S_t^{(1)} = r S_t^{(1)} dt + \\sigma S_t^{(1)} d W_t$$\n",
    "and recognize that sinceztis a standard Brownian motion so will be−ztandthey will have the same exact distribution.  This means that the equation:\n",
    "$$d S_t^{(2)} = r S_t^{(2)} dt - \\sigma S_t^{(2)} d W_t$$\n",
    "will also generate paths of the same asset.\n",
    "The variance depends on the sign of the covariance of $payoff(S_t^{(1)})$ and $payoff(S_t^{(2)})$. It can increase the eventual variance or decrease it, both case do arise. One sufficient condition to insure variance reduction is the monotony of the payoff function. Then, when using both in the calculation of the final Monte Carlo value the variance of the estimate will be reduced.\n",
    "\n",
    "### 4.2 Delta-based control variates\n",
    "Delta hedging can be summarized succinctly in the following way:  Suppose that at time $t= 0$, we receive $C_0$ the price of an option that pays $C_T$ at time T.  The price of this option at any time $t$ is a function $C(t,S)$. Then, if we hold at any moment in time $\\frac{\\partial C}{\\partial S}(t,S) = \\frac{\\partial C_t}{\\partial S}$ units of stock, then we will be able to replicate the payout of this option $C_T$ at time T. This is in theory since of course we cannot trade continuously. So in practice we perform a partial hedge where we only rebalance at some discrete moments in time say $t_1,t_2,\\cdots,t_N$. The replicating strategy can be expressed as follow:\n",
    "$$W(t_i,S_i) = C(t_0,S_0) e^{r(t_i - t_0)} + \\sum_{j=0}^{i} \\Delta(t_j,S_j) ( S_{j+1} e^{-r(t_{j+1} - t_j )} - S_{j})e^{r(t_i - t_j)} = C(t_i,S_i)$$\n",
    "which is similar to the strategy in the optimal hedged Monte Carlo simulation where the only difference is that in OHMC, we use option and delta hedging to replicate the cash flow and here we do the opposite operation. But when implementing the delta-based control variates, we should move the hedging term to the right hand side which make it identical to the OHMC strategy. Note that here we are assumed to know the delta hedging function. It explains a lot why OHMC can reduce the variance.\n",
    "\n",
    "### 4.3 Optimal hedged Monte Carlo simulation\n",
    "**In conclusion, OHMC is just a control variates method with an optimization on top and it is more practical because we do not have an analytical formula for the hedge sensitivity (i.e. delta, gamma, etc.)**"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 Add Hedging portfolio with the Least Square Monte Carlo (LSM)\n",
    "\n",
    "In order to price Amrican type options, we need to consider the problem of optimal exercise. LSM is a well-defined method to tackle this problem. In contrast, here we only utilize the information of exercise points along each simulation path using cross-sectional regression. Different from the original LSM, here we equipe basis functions to approximate price and hedge at each step similar to OHMC. And discuss independently at the inception.\n",
    "\n",
    "This combination create a magic reaction. Now we can not only price the American options but also hedge it! Moreover, it's model independent, model parameters or construction, dimension doesn't matter at all! We use Black-Scholes and Heston model as examples. What only matters is the underlying price trials. With it, we can calculate the following stuffs.\n",
    "\n",
    "* American options price\n",
    "* American options Greeks\n",
    "* American options optimal exercise boundary\n",
    "\n",
    "Here, Bouchard and Warin concluded two main dynamic strategy in American options pricing, A1 and A2. Besides, I equiped them with a hedging strategy:\n",
    "\n",
    "### 5.1 A1 strategy with optimal exercise time estimate\n",
    "\n",
    "* Initialization: $\\tau(t_J) = T$\n",
    "* Backward induction: \n",
    "* $\\tau(t_j) = t_j \\mathbf{1}_{\\{g(t_j)\\geq C(t_j)\\}} + \\tau(t_{j+1})\\mathbf{1}_{\\{Z(t_j)<C(t_j)\\}}$\n",
    "* Price estimator at 0:$P_0 = E[g(\\tau(t_0),X_{\\tau(t_0)})]$\n",
    "\n",
    "\n",
    "### 5.3 A2 strategy with American values estimate\n",
    "\n",
    "* Initialization: $P_T = g(T,X_T)$\n",
    "* Backward induction: $P_{t_j} = max\\{g(t_j,X_{t_j}),E[P_{t_{j+1}}]\\}$\n",
    "* Price estimator at 0: $P_0$\n",
    "\n",
    "### 5.2 A2b strategy with optimal exercise time estimate and American values estimate\n",
    "\n",
    "* Initialization: $\\tau(t_J) = T$\n",
    "* Backward induction: \n",
    "    * $\\tau(t_j) = t_j \\mathbf{1}_{\\{g(t_j)\\geq C(t_j)\\}} + \\tau(t_{j+1})\\mathbf{1}_{\\{Z(t_j)<C(t_j)\\}}$\n",
    "    * Price estimator at j:$P_j = E[g(\\tau(t_j),X_{\\tau(t_j)})]$ for $j=J,J-1,\\cdots,1$\n",
    "* Price estimator at 0 (one-step hedged MC): ${arg\\,min}_{P_0,H_0} E[(\\Delta W_0)^2]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import scipy.stats\n",
    "from cvxopt import matrix, solvers\n",
    "import binomial\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from MonteCarlo import MonteCarlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "risk_free_rate = 0.06\n",
    "dividend = 0.0\n",
    "time_to_maturity = 1\n",
    "volatility = 0.3\n",
    "strike = 1.1\n",
    "stock_price = 1\n",
    "n_trials = 400\n",
    "n_steps = 20\n",
    "func_list = [lambda x: x**0, lambda x: x] # basis for OHMC part\n",
    "option_type = 'p'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15262237404048512"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binomial.put(S=stock_price, K=strike, sigma=volatility, r=risk_free_rate,\n",
    "             t=time_to_maturity, div=dividend, n=n_steps, am=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1409834432994072"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binomial.put(S=stock_price, K=strike, sigma=volatility, r=risk_free_rate,\n",
    "             t=time_to_maturity, div=dividend, n=n_steps, am=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mc = MonteCarlo(stock_price,strike,time_to_maturity,risk_free_rate,dividend,volatility)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.14018199152981647"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mc.BlackScholesPricer(option_type=option_type) # BS formula for European options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.48711664358348156"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mc.BSDelta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "price_matrix = mc.simulate(n_trials,n_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# # Sanity check\n",
    "# price_matrix = [[1,1.09,1.08,1.34],\n",
    "#                [1,1.16,1.26,1.54],\n",
    "#                [1,1.22,1.07,1.03],\n",
    "#                [1,0.93,0.97,0.92],\n",
    "#                [1,1.11,1.56,1.52],\n",
    "#                [1,0.76,0.77,0.90],\n",
    "#                [1,0.92,0.84,1.01],\n",
    "#                [1,0.88,1.22,1.34]]\n",
    "# price_matrix = np.array(price_matrix)\n",
    "# mc.price_matrix = price_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# mc.LSM3(option_type=option_type,func_list=[lambda x: x**0, lambda x: x],onlyITM=False,buy_cost=0.0,sell_cost=0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price: 0.15106104051425842, delta-hedge: 0.44849620415068886\n"
     ]
    }
   ],
   "source": [
    "mc.LSM(option_type=option_type,func_list=[lambda x: x**0, lambda x: x],onlyITM=False,buy_cost=0.0,sell_cost=0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# mc.LSM2(option_type=option_type,func_list=[lambda x: x**0, lambda x: x],buy_cost=0.0,sell_cost=0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# mc.LSM(option_type=option_type,func_list=[lambda x: x**0, lambda x: x],onlyITM=False,buy_cost=0.05,sell_cost=0.08)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# mc.american_values_matrix,mc.price_matrix,mc.exercise_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1499380767008969"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mc.MCPricer(option_type=option_type,isAmerican=True) # LSM for American options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.14536444436004428"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mc.MCPricer(option_type=option_type,isAmerican=False) # original MC for European options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# mc.OHMCPricer(option_type=option_type,isAmerican=True) # OHLSM for American options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.14256024021081362"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mc.OHMCPricer(option_type=option_type,isAmerican=False) # OHLSM for European options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.5 Performance Test:\n",
    "\n",
    "#### Parameters:\n",
    "\n",
    "    risk_free_rate = 0.06\n",
    "    dividend = 0.0\n",
    "    time_to_maturity = 1\n",
    "    volatility = 0.3\n",
    "    strike = 1.1\n",
    "    stock_price = 1\n",
    "    n_trials = 4000\n",
    "    n_steps = 20\n",
    "    func_list = [lambda x: x**0, lambda x: x] # basis for OHMC part\n",
    "    option_type = 'p'\n",
    "    \n",
    "#### Results:\n",
    "\n",
    "**American Options**\n",
    "\n",
    "|Algorithm | Price  | Delta  |\n",
    "|---|---|---|\n",
    "| A1  | 0.1499 | N/A  | \n",
    "|  A2 |  0.1590 | 0.585  | \n",
    "|  A2b |  0.1500 | 0.491  | \n",
    "\n",
    "\n",
    "**European Options**\n",
    "\n",
    "* BS Formula: 0.1401\n",
    "* BS Binomial Tree: 0.1410\n",
    "* Regular MC: 0.1453\n",
    "* OHMC: 0.1426"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6 Early Exercise Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mc = MonteCarlo(S0=stock_price,K=1,T=time_to_maturity,r=risk_free_rate,q=dividend,sigma=volatility)\n",
    "price_matrix = mc.simulate(n_trials,n_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price: 0.15535896988712722, delta-hedge: -0.7567046868819357\n"
     ]
    }
   ],
   "source": [
    "mc.LSM(option_type='c',func_list=[lambda x: x**0, lambda x: x],onlyITM=False,buy_cost=0.0,sell_cost=0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.15535896988712722, 0.7567046868819357)"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mc.HLSM_price,mc.HLSM_delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "K1 = 0.9\n",
    "K2 = 1.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def earlyExerciseComparison(S0,K,T,r,q,sigma,option_type):\n",
    "    metric_dict = dict()\n",
    "    mc = MonteCarlo(S0,K,T,r,q,sigma)\n",
    "    price_matrix = mc.simulate(n_trials,n_steps)\n",
    "    mc.LSM(option_type=option_type,func_list=[lambda x: x**0, lambda x: x],onlyITM=False,buy_cost=0.0,sell_cost=0.0)\n",
    "    metric_dict[\"BS price\"] = mc.BlackScholesPricer(option_type)\n",
    "    metric_dict[\"BS delta\"] = mc.BSDeltaHedgedPricer(option_type)\n",
    "    metric_dict[\"price\"] = mc.HLSM_price\n",
    "    metric_dict[\"delta\"] = mc.HLSM_delta\n",
    "    metric_dict[\"average exercise time\"] = np.where(mc.exercise_matrix==True)[1].mean()/n_steps*time_to_maturity\n",
    "    return metric_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price: 0.1456722164557313, delta-hedge: 0.5059954279887573\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'average exercise time': 0.73025000000000007,\n",
       " 'delta': -0.5059954279887573,\n",
       " 'price': 0.1456722164557313}"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "earlyExerciseComparison(stock_price,strike,time_to_maturity,risk_free_rate,dividend,volatility,'p')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>r</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     r  price\n",
       "0  0.0      1\n",
       "1  0.1      2\n",
       "2  0.2      3\n",
       "3  0.3      4\n",
       "4  0.4      5\n",
       "5  0.5      6"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"price\"] = [1,2,3,4,5,6]\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def averageExerciseTimeRiskFreeRate(S0,K1,K2,T,r_list,q,sigma,option_type):\n",
    "    df1 = pd.DataFrame()\n",
    "    df2 = pd.DataFrame()\n",
    "    df1[\"r\"] = pd.Series(r_list)\n",
    "    df2[\"r\"] = pd.Series(r_list)\n",
    "    price_list1 = []\n",
    "    delta_list1 = []\n",
    "    exercise_list1 = []\n",
    "    price_list2 = []\n",
    "    delta_list2 = []\n",
    "    exercise_list2 = []\n",
    "    BS_price_list1 = []\n",
    "    BS_price_list2 = []\n",
    "    BS_delta_list1 = []\n",
    "    BS_delta_list2 = []\n",
    "    \n",
    "    for r in r_list:\n",
    "        metric_dict1 = earlyExerciseComparison(S0,K1,T,r,q,sigma,option_type)\n",
    "        metric_dict2 = earlyExerciseComparison(S0,K2,T,r,q,sigma,option_type)\n",
    "        price_list1.append(metric_dict1[\"price\"])\n",
    "        BS_price_list1.append(metric_dict1[\"BS price\"])\n",
    "        delta_list1.append(metric_dict1[\"delta\"])\n",
    "        exercise_list1.append(metric_dict1[\"average exercise time\"])\n",
    "        BS_delta_list1.append(metric_dict1[\"BS delta\"])\n",
    "        BS_delta_list2.append(metric_dict2[\"BS delta\"])\n",
    "        price_list2.append(metric_dict2[\"price\"])\n",
    "        BS_price_list2.append(metric_dict2[\"BS price\"])\n",
    "        delta_list2.append(metric_dict2[\"delta\"])\n",
    "        exercise_list2.append(metric_dict2[\"average exercise time\"])\n",
    "    df1[\"price\"] = price_list1\n",
    "    df1[\"BS price\"] = BS_price_list1\n",
    "    df1[\"delta\"] = delta_list1\n",
    "    df1[\"average exercise time\"] = exercise_list1\n",
    "    \n",
    "    df2[\"price\"] = price_list2\n",
    "    df2[\"BS price\"] = BS_price_list2\n",
    "    df2[\"delta\"] = delta_list2\n",
    "    df2[\"average exercise time\"] = exercise_list2\n",
    "    \n",
    "    df1[\"BS delta\"] = BS_delta_list1\n",
    "    df2[\"BS delta\"] = BS_delta_list2\n",
    "    \n",
    "    return df1,df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def averageExerciseTimeDividend(S0,K1,K2,T,r,q_list,sigma,option_type):\n",
    "    df1 = pd.DataFrame()\n",
    "    df2 = pd.DataFrame()\n",
    "    df1[\"dividend\"] = pd.Series(q_list)\n",
    "    df2[\"dividend\"] = pd.Series(q_list)\n",
    "    price_list1 = []\n",
    "    delta_list1 = []\n",
    "    exercise_list1 = []\n",
    "    price_list2 = []\n",
    "    delta_list2 = []\n",
    "    exercise_list2 = []\n",
    "    BS_price_list1 = []\n",
    "    BS_price_list2 = []\n",
    "    BS_delta_list1 = []\n",
    "    BS_delta_list2 = []\n",
    "    \n",
    "    for q in q_list:\n",
    "        metric_dict1 = earlyExerciseComparison(S0,K1,T,r,q,sigma,option_type)\n",
    "        metric_dict2 = earlyExerciseComparison(S0,K2,T,r,q,sigma,option_type)\n",
    "        price_list1.append(metric_dict1[\"price\"])\n",
    "        BS_price_list1.append(metric_dict1[\"BS price\"])\n",
    "        delta_list1.append(metric_dict1[\"delta\"])\n",
    "        exercise_list1.append(metric_dict1[\"average exercise time\"])\n",
    "        BS_delta_list1.append(metric_dict1[\"BS delta\"])\n",
    "        BS_delta_list2.append(metric_dict2[\"BS delta\"])\n",
    "        price_list2.append(metric_dict2[\"price\"])\n",
    "        BS_price_list2.append(metric_dict2[\"BS price\"])\n",
    "        delta_list2.append(metric_dict2[\"delta\"])\n",
    "        exercise_list2.append(metric_dict2[\"average exercise time\"])\n",
    "    df1[\"price\"] = price_list1\n",
    "    df1[\"BS price\"] = BS_price_list1\n",
    "    df1[\"delta\"] = delta_list1\n",
    "    df1[\"average exercise time\"] = exercise_list1\n",
    "    \n",
    "    df2[\"price\"] = price_list2\n",
    "    df2[\"BS price\"] = BS_price_list2\n",
    "    df2[\"delta\"] = delta_list2\n",
    "    df2[\"average exercise time\"] = exercise_list2\n",
    "    \n",
    "    df1[\"BS delta\"] = BS_delta_list1\n",
    "    df2[\"BS delta\"] = BS_delta_list2\n",
    "    \n",
    "    return df1,df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def averageExerciseTimeVolatility(S0,K1,K2,T,r,q,sigma_list,option_type):\n",
    "    df1 = pd.DataFrame()\n",
    "    df2 = pd.DataFrame()\n",
    "    df1[\"volatility\"] = pd.Series(sigma_list)\n",
    "    df2[\"volatility\"] = pd.Series(sigma_list)\n",
    "    price_list1 = []\n",
    "    delta_list1 = []\n",
    "    exercise_list1 = []\n",
    "    price_list2 = []\n",
    "    delta_list2 = []\n",
    "    exercise_list2 = []\n",
    "    BS_price_list1 = []\n",
    "    BS_price_list2 = []\n",
    "    BS_delta_list1 = []\n",
    "    BS_delta_list2 = []\n",
    "    \n",
    "    for sigma in sigma_list:\n",
    "        metric_dict1 = earlyExerciseComparison(S0,K1,T,r,q,sigma,option_type)\n",
    "        metric_dict2 = earlyExerciseComparison(S0,K2,T,r,q,sigma,option_type)\n",
    "        price_list1.append(metric_dict1[\"price\"])\n",
    "        BS_price_list1.append(metric_dict1[\"BS price\"])\n",
    "        delta_list1.append(metric_dict1[\"delta\"])\n",
    "        exercise_list1.append(metric_dict1[\"average exercise time\"])\n",
    "        BS_delta_list1.append(metric_dict1[\"BS delta\"])\n",
    "        BS_delta_list2.append(metric_dict2[\"BS delta\"])\n",
    "        price_list2.append(metric_dict2[\"price\"])\n",
    "        BS_price_list2.append(metric_dict2[\"BS price\"])\n",
    "        delta_list2.append(metric_dict2[\"delta\"])\n",
    "        exercise_list2.append(metric_dict2[\"average exercise time\"])\n",
    "    df1[\"price\"] = price_list1\n",
    "    df1[\"BS price\"] = BS_price_list1\n",
    "    df1[\"delta\"] = delta_list1\n",
    "    df1[\"average exercise time\"] = exercise_list1\n",
    "    \n",
    "    df2[\"price\"] = price_list2\n",
    "    df2[\"BS price\"] = BS_price_list2\n",
    "    df2[\"delta\"] = delta_list2\n",
    "    df2[\"average exercise time\"] = exercise_list2\n",
    "    \n",
    "    df1[\"BS delta\"] = BS_delta_list1\n",
    "    df2[\"BS delta\"] = BS_delta_list2\n",
    "    \n",
    "    return df1,df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def averageExerciseTimeDividend(S0,K1,K2,T,r,q_list,sigma,option_type):\n",
    "    averageExerciseTime1_list = []\n",
    "    averageExerciseTime2_list = []\n",
    "    for q in q_list:\n",
    "        averageExerciseTime1_list.append(earlyExerciseComparison(S0,K1,T,r,q,sigma,option_type))\n",
    "        averageExerciseTime2_list.append(earlyExerciseComparison(S0,K2,T,r,q,sigma,option_type))\n",
    "    return averageExerciseTime1_list,averageExerciseTime2_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def averageExerciseTimeVolatility(S0,K1,K2,T,r,q,sigma_list,option_type):\n",
    "    averageExerciseTime1_list = []\n",
    "    averageExerciseTime2_list = []\n",
    "    for sigma in sigma_list:\n",
    "        averageExerciseTime1_list.append(earlyExerciseComparison(S0,K1,T,r,q,sigma,option_type))\n",
    "        averageExerciseTime2_list.append(earlyExerciseComparison(S0,K2,T,r,q,sigma,option_type))\n",
    "    return averageExerciseTime1_list,averageExerciseTime2_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.1 risk free rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r_low=0.1\n",
    "r_high=0.5\n",
    "r_list = [0.1*i for i in range(5)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price: 0.07344334026203707, delta-hedge: 0.2851610642518651\n",
      "price: 0.2543805207332204, delta-hedge: 0.8191544939879063\n",
      "price: 0.05067828994004845, delta-hedge: 0.24495187445857697\n",
      "price: 0.2045990306193768, delta-hedge: 0.7971059352201469\n",
      "price: 0.02499356625533608, delta-hedge: 0.10579438462464796\n",
      "price: 0.1889819157676027, delta-hedge: 0.968548439020071\n",
      "price: 0.014992853067425288, delta-hedge: 0.12824733152197199\n",
      "price: 0.18278239380047767, delta-hedge: 0.9725999045284608\n",
      "price: 0.011631876772482086, delta-hedge: 0.08490543391511093\n",
      "price: 0.17706993164488505, delta-hedge: 0.954046544479705\n"
     ]
    }
   ],
   "source": [
    "r_df1,r_df2 = averageExerciseTimeRiskFreeRate(S0=stock_price,K1=K1,K2=K2,T=time_to_maturity,r_list=r_list,q=dividend,sigma=volatility,option_type=\"p\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "r_put_ITM_df = r_df2\n",
    "r_put_OTM_df = r_df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>r</th>\n",
       "      <th>price</th>\n",
       "      <th>BS price</th>\n",
       "      <th>delta</th>\n",
       "      <th>average exercise time</th>\n",
       "      <th>BS delta</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.254381</td>\n",
       "      <td>0.254406</td>\n",
       "      <td>-0.819154</td>\n",
       "      <td>0.816125</td>\n",
       "      <td>0.256058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.204599</td>\n",
       "      <td>0.171868</td>\n",
       "      <td>-0.797106</td>\n",
       "      <td>0.359750</td>\n",
       "      <td>0.172237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.188982</td>\n",
       "      <td>0.109633</td>\n",
       "      <td>-0.968548</td>\n",
       "      <td>0.092500</td>\n",
       "      <td>0.111145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.3</td>\n",
       "      <td>0.182782</td>\n",
       "      <td>0.065586</td>\n",
       "      <td>-0.972600</td>\n",
       "      <td>0.074500</td>\n",
       "      <td>0.065962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.4</td>\n",
       "      <td>0.177070</td>\n",
       "      <td>0.036569</td>\n",
       "      <td>-0.954047</td>\n",
       "      <td>0.053875</td>\n",
       "      <td>0.036136</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     r     price  BS price     delta  average exercise time  BS delta\n",
       "0  0.0  0.254381  0.254406 -0.819154               0.816125  0.256058\n",
       "1  0.1  0.204599  0.171868 -0.797106               0.359750  0.172237\n",
       "2  0.2  0.188982  0.109633 -0.968548               0.092500  0.111145\n",
       "3  0.3  0.182782  0.065586 -0.972600               0.074500  0.065962\n",
       "4  0.4  0.177070  0.036569 -0.954047               0.053875  0.036136"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_put_ITM_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>r</th>\n",
       "      <th>price</th>\n",
       "      <th>BS price</th>\n",
       "      <th>delta</th>\n",
       "      <th>average exercise time</th>\n",
       "      <th>BS delta</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.073443</td>\n",
       "      <td>0.070129</td>\n",
       "      <td>-0.285161</td>\n",
       "      <td>0.945875</td>\n",
       "      <td>0.070197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.050678</td>\n",
       "      <td>0.039454</td>\n",
       "      <td>-0.244952</td>\n",
       "      <td>0.924375</td>\n",
       "      <td>0.039866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.024994</td>\n",
       "      <td>0.020587</td>\n",
       "      <td>-0.105794</td>\n",
       "      <td>0.868500</td>\n",
       "      <td>0.021246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.3</td>\n",
       "      <td>0.014993</td>\n",
       "      <td>0.009914</td>\n",
       "      <td>-0.128247</td>\n",
       "      <td>0.851250</td>\n",
       "      <td>0.009300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.4</td>\n",
       "      <td>0.011632</td>\n",
       "      <td>0.004387</td>\n",
       "      <td>-0.084905</td>\n",
       "      <td>0.854000</td>\n",
       "      <td>0.004158</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     r     price  BS price     delta  average exercise time  BS delta\n",
       "0  0.0  0.073443  0.070129 -0.285161               0.945875  0.070197\n",
       "1  0.1  0.050678  0.039454 -0.244952               0.924375  0.039866\n",
       "2  0.2  0.024994  0.020587 -0.105794               0.868500  0.021246\n",
       "3  0.3  0.014993  0.009914 -0.128247               0.851250  0.009300\n",
       "4  0.4  0.011632  0.004387 -0.084905               0.854000  0.004158"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_put_OTM_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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TOqS0LBj7CJxwK3z5L5gyAr77LOiqRNqFJsPdOVcBXAm8BiwAnnHOfWZmE8xs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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c757898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r_list,r_put_OTM_df[\"average exercise time\"],label=\"put option, OTM\")\n",
    "plt.plot(r_list,r_put_ITM_df[\"average exercise time\"],label=\"put option, ITM\")\n",
    "plt.legend()\n",
    "plt.title(\"r vs. average exercise time\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/+lcSlj6FvbiYrLlzyfvzn3E4n6/aX/T1sswddcEFF/CHP/yBX/ziF8e0n/5M\nAr/o8UIzMhj60YdE/OpXFD2/jL2zz6fyu+993axu0x/KMndEaGgot99+O35+fse0n/5M9cR502lp\naTozM9PXzRA9UOV333Povvuoz8kh4qKLGPD72zC3c5Z5LLZv386YMWO6bP/tycrK4txzz+3yQm2L\nFy9udUDYW7Zs2cKyZcukQqcXtPR3qZTa6GkFZDnjF71K8NQpDH3/PaKuWUDJO+8YZR9WrfJ1s4QH\npCxzzyFn/KLXqv5pC4fuuYfanTsJPetM4u++G0tMjFeP4eszfiFaImf8ot8KHD+OIW+/RezvbqJi\n5Sp+PudcSt57T8o+CNEOCfyiV1NWKzELFzLk/ffwHzaMQ3fcyf7/+3/U5R7bzBEh+jIJ/KJP8B86\nlORXXibu3nuo/vFH9p53HkUvv4K2233dNCF6HAn8os9QJhNRl1/O0I8+JOjEE8n74x/JvvwKavfs\n8XXThOhRJPCLPsc6aBCJz/6TQX96jLp9+9h3wYXkP/00uq7O103rFLPZ7CpPnJqayqOP+uYOYl9Y\nvnw5Bw8e9Mq+mperfuaZZ3jppZe8sm93ubm5zJ49mxEjRjBs2DBuuukm6urq+Oyzz1z/hiEhIYwa\nNYrU1FTmz5/P2rVrUUrx3HPPufazadMmlFIsWbLE622UwC/6JKUU4eedx9D/fEzo6adT8OTf2Tfn\nIqp/8nKRtW4QGBjIpk2bXF933HGHx9t6s1SCL3Rl4F+4cCHz58/3yr4baK258MILOf/889m9eze7\ndu2ioqKCu+++m1/84heuf8O0tDRWrFjBpk2bXMln3LhxvPnmm659vfbaaxx/fNdUtZfAL/o0S3Q0\ng//6FxKefhp7aSlZcy8h77E/9YmyDy2VZYbGEsvTpk1j3rx51NTUcPXVVzN+/HgmTpzImjXG4y6X\nL1/O7NmzmTFjBiNGjOD+++937fuVV15h8uTJpKam8utf/xq7c6zkuuuuIy0tjbFjx7Jo0aImbVm0\naBEnnHAC48ePZ8eOHUe1t7XjZWVlNXmYypIlS1i8eDFvv/02mZmZXH755aSmplLd7N9s06ZNTJ06\nlQkTJnDBBRdQXFwMGA91uemmm1wPaVm/fn2L5aoXL17sOptua1+33347kydPZuTIkUfdCd3c6tWr\nCQgI4OqrrwaM3trjjz/OsmXLXOW0W5OcnExNTQ15eXlorfn0008566yz2tyms6RIm+gXQmemEzQp\njSNL/kJ34YpTAAAgAElEQVTRCy9QvnIlAx98gOCpUz3ex2PrH2NH0dEB7ViMjhrN7ZNvb3Od6upq\nUlNTXe/vvPNO5s6d2+Y227ZtY926dQQGBvKXv/wFpRQ//fQTO3bs4IwzzmDXrl0ArF+/ni1bthAU\nFMSkSZM455xzCA4O5o033uDrr7/GarVy/fXXs2LFCubPn88f//hHoqKisNvtZGRksHnzZiZMmABA\nTEwMP/zwA08//TRLlixpctmiQUvHi2nl3os5c+bw1FNPsWTJkhYf/jJ//nz+/ve/c9ppp3Hfffdx\n//3387e//Q2AqqoqNm3axJdffsmCBQvYsmXLUeWqV7nd+NfWvmw2G+vXr+c///kP999/PytXrmz1\n975161ZOPPHEJp+FhYWRlJTEnj17XL+r1syZM4e33nqLiRMncsIJJzQpdudNEvhFv2EODWXg/YsJ\nO+dsDt17LzlXXU34nF8R94c/dGnZh2PVcKmnI8477zwCAwMBo3zyjTfeCMDo0aNJTk52Bf7TTz+d\n6OhoAC688ELWrVuHxWJh48aNTJo0CTASz4ABAwB48803efbZZ7HZbBw6dIht27a5gtmFF14IwIkn\nnsi///3vFtvV0vHOP//8Dv1sAKWlpZSUlHDaaacBcOWVV3LRRRe5ljc8oOXUU0+lrKyMkpKSTu/L\n/efKysrqcFs74uKLL2bu3Lns2LGDSy+91GuP0GxOAr/od4InT2bo++9TsHQphcteoPKLL4m7717C\nTj+9ze3aOzPvbm2VZQ4ODvZoHy2VYtZac+WVV/LII480WbZv3z6WLFnChg0biIyM5Kqrrmpy3Iaz\n07bKMLd0PPefo6WfpTO6osS0J+WljzvuON5+++0mn5WVlZGTk8Pw4cPbPVZ8fDxWq5XPP/+cJ554\nossCv1zjF/2SKSCAAbfeSsqbb2COieHAjb8l96bfYcvP93XTPNZaWebm3Msn79q1i5ycHEaNGgXA\n559/TlFREdXV1bz33ntMmzaNjIwM3n77bY4cOQIYj1jMzs6mrKyM4OBgwsPDycvL45NPPulwm1s6\nXlxcHEeOHKGwsJDa2lrX076g9RLT4eHhREZGuq65v/zyy64zdsD1eMZ169YRHh5OeHh4p/fVkgMH\nDpCRkXHU5xkZGVRVVbkGbO12O7feeitXXXWVxw+NeeCBB3jssceaVFz1NjnjF/1a4NixDHnzDQqX\nvUDB0qX8/N13xN1+O+EXnH9MZ4ne1Pwa/5lnnsmjjz7KokWLuOaaa7j33ntdA7stuf7667nuuusY\nP348FouF5cuXu85iJ0+ezK9+9Styc3O54oorXNfSH3roIc444wwcDgdWq5WlS5cydepUJk6cyOjR\no5s8FawjWjvefffdx+TJkxk8eDCjR492rX/VVVexcOFCAgMD+fbbb12XrwBefPFFFi5cSFVVFUOH\nDuWFF15wLQsICGDixInU19ezbNkywChXPWfOHN5//33+/ve/N2lXW/tqyaFDh7BYjg6fSineffdd\nrr/+eh588EEcDgdnn302Dz/8sMe/o5NPPtnjdTtLirQJ4VS7dx+H7r2X6o0bCT75ZOIfeICfy8v6\nbJG25cuXk5mZyVNPPdWnjjdjxoxWB4S95amnniIpKYnzzjuvy47RFinSJoSX+A8dQvLLLxF3371U\nb9rE3l/+EkdFhRR9E0e54YYbfBb0vUHO+IVoQf3Bgxy6/35KLr6YUSkpWAcPxhQQ4OtmCQHIGb8Q\nXcI6aBCJzzyDOSISXVdH7c8/U3/kCNpt9okQvZUEfiFaoZTCFBSI/4gRmMPCsB05Qu3u3dgKC6Xq\np+jVZFaPEO1QFgt+iYnYIyKw5edTf+gQtiNHMEdFYYmORrUwu0OInkz+YoXwkDk0FHNoKPbKKuyF\nBdjy87EVFGCOiMQSE42pi26vF8Lb5FKPEB1kDg7CLynJuAQUEYG9pJja3bupy8nB0U4hrk4dT8oy\ne2Vf3VWWOSQkhJ9++sn17xUVFcWQIUNITU1l1qxZZGVloZTinnvucW1TUFCA1Wrlhhtu8Hp7WiJn\n/EJ0ksnfH7/Bg9EDBmArKsJeVERtWRmmoCAsMTGYQkO9chNYZ2r1NLDZbC3eaNRbLF++nHHjxjFo\n0KBj3tfatWsJCQlx3SC1cOHCY95na8aPH+/6N7vqqqs499xzmTNnDmBUIx0yZAgff/wxDz30EABv\nvfUWY8eO7bL2NOfRGb9S6kyl1E6l1B6l1FHFwJVSo5VS3yqlapVSt3VkWyF6O2W1Yo2Lw3/kSKzx\nA9H19dTl5FC7Zw+2oqIumwkkZZl7XllmTwUFBTFmzBgapq2/8cYbXHzxxV7ZtyfaPRVQSpmBpcDp\nQC6wQSn1gdZ6m9tqRcBvgfM7sa0QvcLhhx+mdnv7ZZk1gM2Grq9HOxzGWb/VirJYjuoB+I8ZTfxd\nd7W5PynL3HvKMnfEJZdcwuuvv05cXBxms5lBgwZ57bJWezzpA04G9mit9wIopV4HZgOu4K21PgIc\nUUqd09FthehrFIDFAhYLym43EkBdHbq+3gj+VmuHLgFJWeaj9YWyzGeeeSb33nsvcXFx7SZyb/Mk\n8A8G9ru9zwWmeLh/j7dVSl0LXAuQlJTk4e6F6D7tnZm3xVFTg62gAHtpKWgwh4cbM4Hcio51lJRl\nbp2vyjJ3hJ+fHyeeeCJ/+ctf2LZtGx988IHX9t2eHjOrR2v9rNY6TWudFhsb6+vmCOFVpoAA/BIS\n8B8xAkt0FI7yMmp//pnarCzsnawHJGWZe15Z5o669dZbeeyxx4iKijrmfXWEJ2f8B4BEt/cJzs88\ncSzbCtHnmPz8MA0ciKVhJlBhIXVZWZgCAjDHxGAOC0OZmp6PSVnm3lOWuaPGjh3brbN5GrRbpE0p\nZQF2ARkYQXsDcJnWemsL6y4GKrTWSzq6rTsp0iZ6ipaKYXmTdjiwl5ZiKyhA19airFYs0dGYIyNR\nXfggDpCyzMeit5dlbjdlaa1tSqkbgM8AM7BMa71VKbXQufwZpVQ8kAmEAQ6l1O+A47TWZS1t24Gf\nT4g+TZlMWCIjMUdE4Cgvx1ZQQP3hw9jy8zFHRmGJjkJZrb5upmimu2606ipSllmINnT1GX9LHFVV\nxkBwWRkohTkiwrghTEpCCKcuP+MXQnQvU5BREsJRW4utsBB7cTH24mKjVlBMDKagoB7zWEjRO0ng\nF6IdWmufBFqTvz9+gwYZJSEKi7AXFWLftw9TYKDRAwgLkwTQD3njKk2Pmc4pRE8UEBBAYWGhTx+/\nqCwWrHED8B81CuvAgWi7nbr9+41nA3RhSQjR82itKSwsJOAYnwYnZ/xCtCEhIYHc3Fzy8/N93ZRG\nWuOoq8NRVITevx9MJkzBwZiCg4+aCir6noCAABISEo5pHxL4hWiD1WplyJAhvm5Gi7TWVG3YQNHz\ny6j44gtUYCARF15I1NVX4XeMgUH0bTKrR4g+oHb3bgpfWE7phx+C3U7Ymb8gasE1BI7r/puDhG90\nZFaPBH4h+pD6vDyKX36Z4tffwFFRQdCUKURfs4DgU06RgeA+TgK/EP2cvaKCkjffouill7AdPoz/\niBFELVhA+Dlno/z8fN080QUk8AshANB1dZR98gmFzy+jdtcuLHFxRM2fT8TcizGHhPi6ecKLJPAL\nIZrQWlO5bh2Fzy+j6rvvMIWEEDH3YqLmz8caF+fr5gkvkMAvhGhV9ZatFC1bRtmnn4LZTPg55xC1\n4GoCRo70ddPEMZDAL4RoV11uLkXLX6TknXfQ1dUEn3Yq0QuuIWjyJBkI7oUk8AshPGYrLqbk9dcp\nemUF9sJCAsaNI/qaBYSefjrKCzXnRfeQwC+E6DBHTQ2l739A0QsvUJeVhTUhgairriLiwgswBQX5\nunmiHf028L/4TRZJUUGckBxJeKDUMBeiM7TDQcXq1RQ+9zzVmzZhjogg8rLLiLzicizd/IhA4bl+\nGfhrbXaOv/+/1NQ7UApGxYUyeUgUaSlRTE6JIj782IoaCdEfVf3wA4XPL6Ni1SqUvz/hF5xP9NVX\n45ec7OumiWb6ZeAHqKyt53+5pWzYV0xmdhEbs4upqrMDkBAZyOQUZyIYEsmw2BAZwBLCQ7V791L0\nwguUvvc+2mYjdNYsov/vGgKPP97XTRNO/TLwa625/D+XMyR8CLOSZnHSoJOwKD+2HSpjQ1YxG/YV\nkZldREFFHQCRQVZXbyAtJZJxg8OxmqWyoRBtseXnU/TKCopfew1HWRmBaScSveAaQmacJpVBfaxf\nBv5qWzUPfvsga3PXUl5XTqAlkOmDp5ORlMGpCacS6heK1pp9BZVkZhWzPquIzKwisgqrAAiwmpiY\nGMmkIUYymJgUQbC/zGgQoiWOykpK3nmHwuXLsR08hN/QoUQvuJqw887DJCUhfKJfBv4G9Y56Nhze\nwOqc1azKWUVBdQEWk4WpA6eSkZRBemI60YHRrvWPlNWQmV3M+n1FbMgqYvuhMhwazCbF2EFhpCUb\nl4bSUqKICZFnngrhTtfXU/bpZxQuW0bt9u2YY2OImjefyEvmYg4L83Xz+pV+HfjdObSDzfmbWZWz\nipXZK8mtyMWkTKTGpjIreRYZSRkMChnUZJvymnp+yCkhM6uI9fuK2LS/hFqb8YSjoTHBpKVEMikl\nikkpUSRHy7NPhQDnswG+/ZbC55dR+fXXmIKCiLjoIiKvuBy/xERfN69fkMDfAq01u4p3GUkgZyW7\ni3cDMCZqDLOSZzEraRZDI4YetV2dzcFPB0rJzDJ6BBuyiimtrgcgNtTfNUYwKSWKMQPDMJskEYj+\nrWbHDgqXLaPsP5+AzYb/yJGEpKcTmj6DgAkTZCygi0jg90BOWY4rCWzO3wxASliKqycwNnpsi2fz\nDodmT34F6/cVOZNBMQdKqgEI8bdwQnIkk5KNsYLUxAgCrOYu/TmE6KnqDx2i7NPPqFi9mqoffgC7\nHXN0NCGnnUZI+gxCTj4ZU3Cwr5vZZ0jg76C8yjzW7F/DqpxVbDi8Abu2Ex8cz8zEmcxKnsXEAROx\nmFof6D1QUt3YI9hXzM68cgCsZsX4weFMGhLFpGSjZxARJANfov+xl5RQ8dU6KtasoeKrr3CUl6P8\n/AiaOoXQ9HRC0tOxxsf7upm9mgT+Y1BaW8oXuV+wMnsl3xz8hlp7LRH+EaQnpjMreRZTBk7B39z2\nIG9JVR0bsxtmDhWzObeEervxex4ZF8KklCjXzWWDIwK748cSosfQ9fVUbfyBijWrKV+zlvqcHAD8\nx4xxJYGAscfJJaEOksDvJVX1VXx98GtWZq/ky9wvqaivIMgSxKkJp5KRnMEpg08h2Np+V7Wm3s7/\n9pe4xgg2ZhdTUWsDYHBEYJMB4xEDQjDJOIHoJ7TW1O3dS8WaNZSvWUv1jz+Cw4ElNpaQGTMISU8n\n+KSpmALlBKk9Evi7QL29nu8Pf8/K7JWs2b+Gopoi/Ex+nDToJDKSMpiROIPIgEiP9mV3aLYfKnON\nEazPKiK/vBaAiCAracnG9NFJKVGMHxyOn0XOfET/YCsupuKLL6hYs5bKdetwVFaiAgIIPukkY1xg\nxgysAwb4upk9kgT+LmZ32NmUv4mV2StZnbOag5UHMSkTaXFpzEyaSUZSBvHBnl+v1FqTU1TlusN4\nQ1YRewsqAfC3mEhNjDB6BEOiOCEpgtAAKUAn+j5dV0flhg1UrFlLxerV1B88CEDAuHGEpM8gND0d\n/zFjZEq1kwT+bqS1ZnvRdlblrGJV9ip+Lv0ZgHHR48hIzmBW0ixSwlM6vN+CilpXj2BDVhFbD5Zh\nd2hMCsYMDHNdGpqUEsmAMClAJ/o2rTW1u3Ybg8Nr1lC9eTNojWXgQEJmnEZoejpBU6Zg8u+/N1lK\n4PehfaX7XElgS+EWAIaFDyMjOYOMpAzGRHXuDKWy1saPOQ3jBEX8mFNCdb1RgC45OsiVBCalRDEk\nJljOgkSfZisooOKLL6lYu4aKdV+jq6tRQUEEn3wSoekzCZlxGpbo6PZ31IdI4O8hDlceZlXOKlbn\nrCYzLxOHdjAoeBAzk4xpoqmxqZhNnZvnX293sPVgmevSUGZ2MUWVRgG6mBA/0pKNS0OTUiI5bmAY\nFilAJ/ooR20tVd9/T/maNVSsWYvt8GFQisAJEwhxzhLyHzmiz58MeT3wK6XOBJ4AzMBzWutHmy1X\nzuVnA1XAVVrrH5zLsoBywA7YPGlYXwn87oprilm7fy2rclbxzcFvqHfUExUQ1ThNNH4KVnPnr91r\nrfk5v9LVI9iQVcT+IuPGsiA/MyckRbp6BROTIgn0kxvLRN+jtaZ2xw7KV6+mYs1aarYYvW7r4MHO\nJDCD4EmTUH2wkJxXA79SygzsAk4HcoENwKVa621u65wN3IgR+KcAT2itpziXZQFpWusCT3+Avhj4\n3VXWV/LVga9Ylb2KL3O/pMpWRYg1hFMTTmVW8iymDZpGkPXYH3V3uLTG6A1kFbE+q5gdh8vQGiwm\nxdjB4UxOiWTq0GimDI0mRCqRij6oPu8IFV+sNWYJffMNurYWU3AwwdOnEzozneBTT8US6dlsvJ7O\n24H/JGCx1voXzvd3AmitH3Fb55/AWq31a873O4EZWutDEvjbVmuv5ftDjdNES2pL8Df7c/Kgk5mV\nPIvTEk4j3D/cK8cqra7nhxznswmyitmUW0KdzYHFpJiYFMG04TFMHx7D8YkR8mwC0ec4qqup/PY7\nY4B47Vps+flgMhE4cSKh6cY9A35Dh/baS0LeDvxzgDO11v/nfD8PmKK1vsFtnY+AR7XW65zvVwG3\na60zlVL7gFKMSz3/1Fo/28pxrgWuBUhKSjoxOzvbk/b3KTaHjR+P/MjK7JWsyllFXlUeZmVmUvwk\nMpIymJk0kwFB3pvDXFNv54ecYtbtLuDrPQVsPlCK1kbNoalDo5g2PIZTRsTI08pEn6MdDmq2bnPe\nOLaG2u3bAbAmJbnuHg468QSUtfdMne5pgX+w1vqAUmoA8Dlwo9b6y7aO2Z/O+FujtWZr4VZXSems\nsiwAjo89nowkY4ZQUliSV49ZUlXHtz8Xsm6PkQgaHlITF+bvSgLThsXI9FHR59QfOkTF2rWUr1lD\n1Xffo+vqMIWFETJ9ujE2cOopmMO90/PuKj3qUk+zfS0GKrTWS9o6pgT+o+0t2cvKnJWszF7J9iLj\n7GRE5AhmJRnVREdGjvT6Wfn+oiq+3lPgSgTFVUY56pFxIUwfHsv0EdFMHiLjA6JvcVRWUvntt5Sv\nXkPFF19gLywEs5mgE090lZf2S0nxdTOP4u3Ab8EY3M0ADmAM7l6mtd7qts45wA00Du4+qbWerJQK\nBkxa63Ln68+BB7TWn7Z1TAn8bTtQcYDVOatZmb2SH4/8iEaTEJLgKik9IXYCJuXda/QOh2bboTJX\nIli/r4ha5/jACUmRxvjAiGiOT4iQqaOiz9AOBzWbN1O+Zi0Va9ZQu2sXAH5DhhAyM53Q9HQCU1NR\nFt+f/HTFdM6zgb9hTOdcprX+o1JqIYDW+hnndM6ngDMxpnNe7bzMMxR417kbC/Cq1vqP7R1PAr/n\nCqoLXNNEvzv0HTaHjdjAWNIT08lIzmBS/CSsJu9fp6ypt/NDdjFfOXsDPzUZH4hm+vBopsv4gOhj\n6nIPuO4ertywAerrMYeHE3zaqYSmpxM8fTrm0FCftE1u4OqnyuvK+TL3S1blrGLdgXVU26oJ9Qtl\nRsIMMpIzOHnQyQRauqbKYUlVHd+4jQ9kO8cH4sMCXL2BacNjGBAq4wOib7BXVFC57msjEXzxBfaS\nErBaCZ6URsiMdEJmpuOXkNBt7ZHAL6ix1fDtwW9ZmbOStfvXUlZXRqAlkGmDppGRnMGpCacS5td1\nD8PeX1TFOudloW/cxgdGxYW6BoonD4kiWMYHRB+g7XaqN21ylZeu+9mo2eU/Yjgh6TMJSZ9B4IQJ\nKHPX3TgpgV80Ue+oZ2PeRuNegZw1HKk+gsVkYUr8FKYOnMqY6DGMjhrttfsFmmsYH1i3p4B1uwtY\nn1Xkun/ghKRIpo+IYdrwGI5PCJfxAdEn1OXkGElg9RqqNm4Emw1zVFTjYyenTfP6Yycl8ItWObSD\nnwp+ctUQyi5rvF8iISSBMdFjOC76OMZEjWFM9BiiAqK83oaaejsbs4v5ynn/wJaDxvhAqL+FKUOj\njWmjw2MYFivF5kTvZy8ro+Krr4zy0l9+iaOsDGW1EjR1qqu8tHXgwGM+jgR+4bHimmK2F21ne+F2\nthVuY3vRdvaX73ctjw+OdyWB46KOY0z0GK/eRAZQXFnHt3sLXYkgp8gYHxgYHuC6m/jk4dEyPiB6\nPV1fT9UPP7oGiOucN6r6jx5tJIGZMwkYN65TJzwS+MUxKasrY2fRTlci2Fa4jazSLDTG30pMYMxR\nyWBg8ECvnZ3nFFa5Bom//rmAEuf4wOj4UFcikPEB0RfU7t3nSgJVP/yAOSyMEV+v69RYgAR+4XVV\n9VXsLHYmg8LtbCvaxt6Svdi18UyACP8IVzJoSAgJoQnHfD+Bw6HZerDMlQgaxgesZsXEpEimD49h\n+ogYJgyW8QHRu9mKi6nbt4+gE07o1PYS+EW3qLHVsLt4t6tXsK1wG7tLdmNzGA+SD7GGMDpqtDFm\n4EwGyWHJnX4GARjjA5lZxc4ZQ/lsPVjmGh+YOqxxfGCoPIxG9DMS+IXP1Nvr2VOyx5UMthduZ2fx\nTmrtxsPkAy2BjIoc5UoGY6LGMDRiaKdvMiuqbKgvlM9XuwvILTaeQTCoYXxgRAwnD4shNrT/PpJP\n9A8S+EWPYnPY2Fe676hB5GqbEaT9TH6MjBzZOKMoegwjIkbgZ+74wzIaxgfW7cnn6z2FlFY3jg9M\nHx7DtBExTBkSRZCfjA+IvkUCv+jxHNpBdlk22wu3N+kdlNeXA2BRFoZHDmdMVGMyGBk5skN3Htsd\nmm0Hy/hqTz5f7ylgQ1axa3zgBOf4wDQZHxB9hAR+0StprcmtyD0qGRTXFgNgUiaGhg9tkgxGR40m\n2OrZjTA19XY2ZBW5Boq3HCgDIDTAwklDjdpC04fHyMPqRa8kgV/0GVpr8qrymkwt3V64nfzqfAAU\niuSw5KOSgSd3IRdV1vHNz0YSkPEB0dtJ4Bd9Xn5V/lFjBocqGx//MDhksOsO5IaE0NZdyFprchrq\nC+0u4Jufjx4fmD4ihvGDw4kK9pMegehxJPCLfqm9u5DjguJc00obkkFsYGyLQdzu0Gw9WOq6mzgz\nq5g6uwMAP7OJAWH+xIUFEB8WQFxYAHFh/sSHBzAgNID4cOPzQL+uK8glRHMS+IVwau8u5OiAaNe0\n0uOijYTQ0l3I1XV2MrOL2J1XQV55DXmlNRwuq+FIWS2Hy2qoqrMfdezQAItbYgggPtzf9bohacSE\n+MnAsvAKCfxCtKG9u5DD/cOblKQ4Lrrtu5C11lTU2sgrq+Fwaa3xvayGPOfX4bJajpTVcKS8Fruj\n6f83k4KYEKO34Oo5hAUwwJkY4sMDiAsNICzQIpeXRJsk8AvRQZ7ehTw0fChxwXHEB8cTF2R8HxA0\nwKNppnaHprCiljxnL8GVGEpryCuvJa+0hrzyGldtIncBVlOTnkJcmL9bT8L4LDbUnwCrXF7qryTw\nC+EFLd2FnFOeQ0ltyVHrhvuHEx8UbyQF5/eGxBAXFEdccJzH9yDU1NudSaHWeTnJSA7ul5YOl9VQ\nZ3MctW1kkPXoBOHsNTT0KqKD/TCZpPfQ10jgF6IL1dhqyKvKI68yj7yqPA5XHm7yPa8yz3Xvgbtw\n//AmycA9KTQkC0+Tg9aa0up6Z8/B2VtoconJSBAFFbU0/y9uMSkGhPo3uZw0wHmJyb0XESLVT3sV\nCfxC+FiNrYYjVUcak0FDYnBLFi0lhzC/sJYTQ8ProDiCrEEet8Nmd5BfUWtcTiqrdRt3aEwQeaU1\nlNfajto22M98VG+hyRhEeAADQv2xyuB0j9CRwC8pXYguEGAJICksiaSwpFbXqbXXttlr2Fq4laKa\noqO2C/MLa9JLaOnSUkNysJhNDAwPZGB42z2JyobBabfLSe5jEOv3FXGkvIZ6e9MTRaUgOtjvqNlK\nDZeYIoP8CLCaCLCYCbCajddWM/4WkwxW+5AEfiF8xN/s71FyOFJ5hMNVh5skhcNVh9tMDqF+oUf3\nHBpeO5OFe88h2N/C0NgQhsaGtNoWh0NTVFXnSgh5ZQ09CePrUGkN/9tfQmFlnWc/v8XUJBkYycGE\nv9WZJNyW+1vc1nMmjobXLSWWxm0aP5OeSSMJ/EL0YP5mfxLDEkkMS2x1nVp7bZPLSs0vKW0r3NZq\ncmh1zCE4/qjkYDIpYkL8iQnxZ+yg1kti1Nrs5Jcbl5VKquqpqXdQU2+nxmZ3va6tt1Njc35eb3db\nx0FtvZ3S6nqOuC+zNb7uLLNJNSYM53f/JomjaTJpnjgat2lMNP7NklbzZNRTB9El8AvRy/mb/UkM\nTSQxtPXkUGevO6q34H5paXvhdgprCo/ariE5tHRpKT4onvjg+KPGHPwtZhIig0iI9HwswlNaa2pt\nDmqbJQNXAnEmk1qbW4JpIfE0JBP35eW1jUmqcXuH647tzvAzmxqTQ7Oeib97D8f5OirYj1vPGOXF\n31jLJPAL0Q/4mf08Sg5tDUjvKNzRcnKwhhpjDM2TQ1Ac0YHRhPiFEGI1vo7l6WsASinXWXU4nXt4\nT0fZHZpaW7ME45Z4alvq0dgcTZJSS9tX1tkorHQ4k4+RtMIDrRL4hRDdx8/sR0JoAgmhCa2uU2+v\ndyUF995DQ7LYWbSTguqCVrcPtAQSag01koFbQgj1CyXYGkyIXwihVuN1qF9ok3VC/Iz1/EzdWyTP\nbFIE+VkI6vhzgXosCfxCCI9ZzVaPksOR6iPkVeZRVFNEeV05FfUVxlfd0d8PVx6moq6C8vpy11PZ\n2mIxWRqThzXkqOTgnkhC/UJb/DzYGtxqCY7+QAK/EMKrrGYrg0MGMzhkcIe3tTlsVNZXHpUcyuvL\nj7F5LQcAAAXdSURBVE4aDcvqyjlYcZCK+gpXknHotq/LK5Srh9E8abj3Ohp6GcHWYFeyCbWGEuxn\nvLeau+dyk7dJ4BdC9BgWk4Vw/3CPHqTTGq011bbqFpNHZX1lYw+k2bKSmhJyy3MprzPWq7HXtHss\nf7N/055FG72OhmTR/BJXoCWw2+9pkMAvhOhTlFIEWYMIsgYxIGhAp/dTb68/qofRkBSOunzllliy\ny7KpqK+gss7ouTSUAG+NSZlcPYr44HhePOvFTrfZUx4FfqXUmcATgBl4Tmv9aLPlyrn8bKAKuEpr\n/YMn2wohRE9kNVuJNEcSGRDZ6X04tIOq+qomCcSVPFq4fGU1dc+lo3YDv1LKDCwFTgdygQ1KqQ+0\n1tvcVjsLGOH8mgL8A5ji4bZCCNEnmZTJNYOJYF+3ppEnw9qTgT1a671a6zrgdWB2s3VmAy9pw3dA\nhFJqoIfbCiGE6EaeBP7BwH6397nOzzxZx5NtAVBKXauUylRKZebn53vQLCGEEJ3RYyayaq2f1Vqn\naa3TYmNjfd0cIYToszwZ3D0AuN/nneD8zJN1rB5sK4QQoht5csa/ARihlBqilPIDLgE+aLbOB8B8\nZZgKlGqtD3m4rRBCiG7U7hm/1tqmlLoB+AxjSuYyrfVWpdRC5/JngP9gTOXcgzGd8+q2tu2Sn0QI\nIYRH5NGLQgjRB3Tk0Ys9ZnBXCCFE9+iRZ/xKqXwgu5ObxwCt14X1HWlXx0i7Okba1TF9sV3JWmuP\npkT2yMB/LJRSmZ52d7qTtKtjpF0dI+3qmP7eLrnUI4QQ/YwEfiGE6Gf6YuB/1tcNaIW0q2OkXR0j\n7eqYft2uPneNXwghRNv64hm/EEKINkjgF0KIfqbXBH6l1JlKqZ1KqT1KqTtaWK6UUk86l29WSp3g\n6bY+bFeWUuonpdQmpZRXb1X2oF2jlVLfKqVqlVK3dWRbH7bLl7+vy53/fj8ppb5RSh3v6bY+bFeX\n/b48bNtsZ9s2OUuuT/d0Wx+2y2d/Y27rTVJK2ZRSczq6rce01j3+C6POz8/AUMAP+B9wXLN1zgY+\nARQwFfje02190S7nsiwgxke/rwHAJOCPwG0d2dYX7eoBv6+TgUjn67N60N9Xi+3qyt9XB9oWQuM4\n4gRgRw/5nbXYLl//jbmttxqj/tmcrvp99ZYz/p76FLBjaVdXarddWusjWusNQH1Ht/VRu7qSJ+36\nRmtd7Hz7HUaJcY+29VG7uponbavQzsiF8eBB7em2PmpXV/L0Z74ReAc40oltPdZbAn+3PAWsm9sF\nxh/cSqXURqXUtV5qk6ft6optu3rfPeX3dQ1GL64z23ZXu6Drfl8et00pdYFSagfwMbCgI9v6oF3g\nw78xpdRg+P/tnbFKY0EUhr9Ti1YiVoJiJ2yxpBIRBAvBYhV8CN/AwmbBF7DRysLSLg9gZ6EgFoos\niIXY2Ajisg+wx2JGEiWJ92rmzpX7fzBkSOZk/vxMDvfOCRnWCWeWl4otS5GDWEQ6Ftz9wcwmgGMz\nu3H3k9yiakx2v8xsiZBgFz4aWyV9dGX3y93bQNvMFoEdYLnK+fsxQFdOz3aBLXf/b2ZJJ/ouV/xf\nOQWsSGwOXbj76+Mj0Cbc0lWlK0Vs0vfO7ZeZ/QAOgF/u/lQmNoOulH4V1tal5QSYMbPxsrEV6sq9\nxlrAkZndAxvAvpmtFYwtx7CLGCka4c7kDpimU9yYezdmlbdF1POisZl0jQCjXf1TYKUqXV1jf/O2\nuJvVrwG6svoFTBEOGpr/7GeqWFcyv0pom6VTRP1JSFZWA8/66arFdzKOP6RT3B26X0NZBFU0wq9j\nbgnV7e343CawGfsG7MXXr4HWoNjcuggV+qvY/mTQNUnYK/wH/I39sRr41VNXDfw6AJ6By9guarK+\neupK7VdBbVtx7kvgjLCNUgfPeurKvcbejT0kJv4UfukvG4QQomF8lz1+IYQQQ0KJXwghGoYSvxBC\nNAwlfiGEaBhK/EII0TCU+IUQomEo8QshRMN4AUdk3N0Ox2E+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d0a1780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r_list,r_put_OTM_df[\"price\"],label=\"put option, OTM\")\n",
    "plt.plot(r_list,r_put_ITM_df[\"price\"],label=\"put option, ITM\")\n",
    "plt.plot(r_list,r_put_OTM_df[\"BS price\"],label=\"European put option, OTM\")\n",
    "plt.plot(r_list,r_put_ITM_df[\"BS price\"],label=\"European put option, ITM\")\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"r vs. price\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UKi4u5v777+faa69l5syZ3HDDDYDVBn/ddddx2223sWTJknD6L37xiyxfvpw1\na9Zw7733cvLJJ4e3tXbQzp07l6ysLB599NHwtrlz53LqqadSVVXFbbfdxtixYykqKsLpdDJv3jyu\nvvpqFixYENexYgmFQuzZs4f8/PwO237+859z8803M23aNBwOB9OnT+e5556LuxYyfvx4vvWtb8WV\nVoGYeN9MnQIlJSVm06ZNqc7GoOULBKlp8FNd76e6wU91vS963p5W1fvZf6QJsDpwT5s+csh24PbW\nzp07mTFjRsrOX1ZWxnnnnce2bdv69DyxbrFMtm3btvHwww/zX/+lXYKJivV3KSKbjTFx3aOrNYBB\nJBgyHG60C/R6H1UNfmrsgryqvq1Qr2nwU1Xvo645dnurx+kgP9tDQY6HghwvU4pymDlmGKfN0A5c\n1fdmz56thf8AoQEghYwx1DYFqGrwhQv16vAVu6/d1M/hRj+xKmwOwSrQs70U5HiYPS6PgmyP9cmx\n1kXO53pdWsgPMpMmTerzq3+wagAqfWgASCJjDI3+INX1/nChXtPgs6/OrcK8JuJqvabBTyAUuwku\nL9NNQY6HwmwvRxflsGiyVYAX5njChX2hfQWfl+nGqQ9VKaV6SANAN5pb2trRqxp81ERclVfZBXzr\nVXtVvQ9fIBTzONkeZ/gKfNzwDOaOyws3wRS0NsfYhfqIbA9uZ0I3aCmlVLfSLgAEgiFqwu3osZta\nIpti6n2dtKO7HBRme8i3C+5jRuZQmOO1r849FLY2vdgFfIZbO1OVUgPLkAsAxhgef/sT++rcKtgj\nm1wON7bE3M/pkHDhXZDjYd6I4dFt59nRV+s52o6ulBrkhlwAEBHu/utu6n0Bhme5wwV38ejcDm3n\n+dkeaz7bakfXwcnUUDIYh4NesmQJK1eu5MYbb8Tn81FTU0NTU1N4ZM/nn3+eJUuWMGHChKhxfubP\nn08gEOiXjvKhZMgFAIC//98lDMt0azu6SmuDcTjoVu+8Y40Yv2rVKjZt2sR9990Xtb2uro59+/Yx\nYcIEdu7c2Wf5GOqGZAlZkOPVwl8NKekwHHRPXHLJJaxevRrQoZ8TMSRrAEr1qb/cCgc/SO4xR8+B\ns+/qMslQHw66Jy6++GKuueYabr75Zv785z/zxBNP8Pvf/z7h46YbvUxWapBoPxz0+vXre32s9evX\nc8UVVwCdDwddWFgYHg66t8dqHQ66sLAwPBx0MhQUFDBixAieeuopZsyYQVZWVlKOm260BqBUT3Vz\npd5XhvpY7/05AAAXPUlEQVRw0D116aWXcuONN7Jq1aqkHTPdaA1AqUFiqA8H3VMXXngh3/3udznz\nzDMTOk460wCg1CDROhz0jBkzOHz4cNRw0DfddBMlJSXhd+mCNRz0c889F7MT+I477mDz5s3MnTuX\nW2+9NeZw0IsXLw4PBz137tzwcND33HNP3MeKpavhoHsiNzeXW265BY/Hk9Bx0pkOB61UHHQ46OTR\n4aCTJ9HhoLUGoJTqVzoc9MChncBKDQI6HLTqC1oDUEqpNKUBQCml0pQGAKWUSlMaAJRSKk1pAFBq\nkHA6ncyfPz/8ueuu1DyRnAqrVq3i008/Tcqx1q1bx4YNG8LLv/3tb3nssceScuxI5eXlLFu2jKlT\np3L00Udz00034ff7eeWVV8L/hjk5ORQXFzN//nyuvPJK1q1bh4jw0EMPhY+zZcsWRISVK1cmPY8J\nBQARyReRV0XkQ3s6oou0ThF5X0ReTOScSqWrzMxMtmzZEv7ceuutce+bzCEYUqEvA8CKFSu48sor\nk3LsVsYYLrroIi644AI+/PBDSktLqa+v5wc/+AFnnnlm+N+wpKSEJ554gi1btoSD0OzZs3n66afD\nx3ryySeZN29eUvPXKtEawK3A68aYqcDr9nJnbgJ04G6lkizWcNDQNrTziSeeyBVXXEFzczPXXHMN\nc+bMYcGCBbzxxhuAVbguW7aMJUuWMHXqVO68887wsR9//HEWLVrE/Pnz+drXvkYwGATghhtuoKSk\nhFmzZnH77bdH5eX222/n2GOPZc6cOezatatDfjs7X1lZGbNnzw6nW7lyJXfccQfPPvssmzZt4vLL\nL2f+/Pk0NTVFHW/Lli0sXryYuXPncuGFF3L48GHAernMTTfdxPz585k9ezYbN26MOUz2HXfcEb66\n7upYt9xyC4sWLWLatGkdnqxub+3atWRkZHDNNdcAVu3tnnvu4eGHHw4P492Zo446iubmZg4dOoQx\nhr/+9a+cffbZXe7TW4k+B7AMWGLPPwqsA25pn0hExgPnAj8Fvp3gOZVKqbs33s2umo4FWyKm50/n\nlkUd/utEaWpqYv78+eHl733ve1x66aVd7rNjxw7Wr19PZmYmv/jFLxARPvjgA3bt2sUXvvAFSktL\nAdi4cSPbtm0jKyuLhQsXcu6555Kdnc3q1at58803cbvdfP3rX+eJJ57gyiuv5Kc//Sn5+fkEg0GW\nLl3K1q1bmTt3LgCFhYW89957PPDAA6xcuTKqOaNVrPMVFhbG/A7Lly/nvvvuY+XKlTFfQnPllVdy\n7733csopp/CjH/2IO++8k1/+8pcANDY2smXLFv7xj39w7bXXsm3btg7DZL/++utxHSsQCLBx40Ze\nfvll7rzzTl577bVOf/ft27dz3HHHRa0bNmwYEydOZM+ePeHfqjPLly/nmWeeYcGCBRx77LFRg+ol\nU6IBYJQx5oA9fxAY1Um6XwLfBXK7O6CIXA9cDzBx4sQEs6fU0NHaBNQT559/PpmZmYA1bPM3v/lN\nAKZPn85RRx0VDgBnnHEGBQUFAFx00UWsX78el8vF5s2bWbhwIWAFoJEjRwLw9NNP8+CDDxIIBDhw\n4AA7duwIF2oXXXQRAMcddxx/+tOfYuYr1vkuuOCCHn03gM8++4wjR45wyimnAHDVVVfxpS99Kby9\n9UUxn//856mtreXIkSO9Plbk9yorK+txXnvikksu4dJLL2XXrl18+ctfjmqySqZuA4CIvAaMjrHp\nB5ELxhgjIh0GFhKR84AKY8xmEVnS3fmMMQ8CD4I1FlB36ZXqb91dqfe3roaDzs7OjusYsYaANsZw\n1VVX8fOf/zxq28cff8zKlSt59913GTFiBFdffXXUeVuvVrsa/jnW+SK/R6zv0ht9MbR1PMNaz5w5\nk2effTZqXW1tLXv37uWYY47p9lyjR4/G7Xbz6quv8qtf/arPAkC3fQDGmNONMbNjfNYAh0RkDIA9\nrYhxiBOB80WkDHgKOE1EHk/id1AqrXU2HHR7kcM2l5aWsnfvXoqLiwF49dVXwy9gf/755znxxBNZ\nunQpzz77LBUV1n/rmpoaPvnkE2pra8nOziYvL49Dhw7xl7/8pcd5jnW+UaNGUVFRQXV1NT6fL/z2\nMeh8aOu8vDxGjBgRbpP//e9/H76CB8KvjVy/fj15eXnk5eX1+lix7N+/n6VLl3ZYv3TpUhobG8Md\nu8FgkO985ztcffXVcb+85sc//jF333131AivyZZoE9ALwFXAXfZ0TfsExpjvAd8DsGsANxtjvprg\neZVKO+37AM466yzuuusubr/9dq677jpuu+22cAdwLF//+te54YYbmDNnDi6Xi1WrVoWvahctWsTF\nF19MeXk5X/3qV8Nt7T/5yU/4whe+QCgUwu12c//997N48WIWLFjA9OnTo95S1hOdne9HP/oRixYt\nYty4cUyfPj2c/uqrr2bFihVkZmby1ltvhZu1AB599FFWrFhBY2MjU6ZM4ZFHHglvy8jIYMGCBbS0\ntPDwww8D1jDZy5cvZ82aNdx7771R+erqWLEcOHAAl6tjMSoiPPfcc3z961/nP//zPwmFQpxzzjn8\n7Gc/i/s3OuGEE+JO22vGmF5/gAKsu38+BF4D8u31Y4GXY6RfArwY7/GPO+44o9RAsGPHjlRnoc88\n8sgj5sYbbxxy5zvllFPMu+++26fnuPfee82aNWv69BxdifV3CWwycZaxCdUAjDHVQIf6jzHmU+Cc\nGOvXYd0ppJRSg943vvGNVGchIfpCGKXikOoXwigVi74QRimlVK9oAFBKqTSlAUAppdKUBgCllEpT\nGgCUGiR0OOjBNRx0Tk4OH3zwQfjfKz8/n8mTJzN//nxOP/10ysrKEBF++MMfhvepqqrC7Xb3291F\n+lJ4pQaJ3owF1CoQCMR8YGmwWLVqFbNnz2bs2LEJH2vdunXk5OSEH7RasWJFwsfszJw5c8L/Zldf\nfTXnnXcey5cvB6zRTydPnsxLL73ET37yEwCeeeYZZs2a1Wf5aU9rAEoNcjoc9MAbDjpeWVlZzJgx\ng9bb3VevXs0ll1ySlGPHY/BeEiiVIgd/9jN8O5M7HLR3xnRGf//7XabR4aAHz3DQPXHZZZfx1FNP\nMWrUKJxOJ2PHjk1ac1d3NAAoNUjocNAdDYXhoM866yxuu+02Ro0a1W1ATzYNAEr1UHdX6v1Nh4Pu\nXKqGg+4Jj8fDcccdxy9+8Qt27NjBCy+8kLRjd0f7AJQa5HQ46IE3HHRPfec73+Huu+8mPz8/4WP1\nhNYAlBokdDjowTMcdE/NmjWrX+/+aaWDwSkVh6E8GNyqVavYtGkT991335A635IlSzrtOE6W++67\nj4kTJ3L++ef32Tm6kuhgcFoDUEqpXtLhoPuQ1gDUQDGUawBq8NLhoJVSSvWKBgCl4jSQa8sq/STj\n71EDgFJxyMjIoLq6WoOAGhCMMVRXV5ORkZHQcbQTWKk4jB8/nvLyciorK1OdFaUA66Jk/PjxCR1D\nA4BScXC73UyePDnV2VAqqbQJSCml0pQGAKWUSlMJBQARyReRV0XkQ3s6opN0w0XkWRHZJSI7ReRz\niZxXKaVU4hKtAdwKvG6MmQq8bi/H8ivgr8aY6cA8YGeC51VKKZWgRAPAMuBRe/5RoMOA3iKSB3we\n+B2AMcZvjOl8UG6llFL9ItEAMMoYc8CePwiMipFmMlAJPCIi74vIQyLS6SDlInK9iGwSkU16y51S\nSvWdbgOAiLwmIttifJZFpjPWEzKxnpJxAccCvzHGLAAa6LypCGPMg8aYEmNMSVFRUc++jVJKqbh1\n+xyAMeb0zraJyCERGWOMOSAiY4CKGMnKgXJjzDv28rN0EQCUUkr1j0SbgF4ArrLnrwLWtE9gjDkI\n7BORYnvVUmBHgudVSimVoEQDwF3AGSLyIXC6vYyIjBWRlyPSfRN4QkS2AvOBnyV4XqWUUglKaCgI\nY0w11hV9+/WfAudELG8B+u61PEoppXpMnwRWSqk0pQFAKaXSlAYApZRKUxoAlFIqTWkAUEqpNKUB\nQCml0pQGAKWUSlMaAJRSKk1pAFBKqTSlAUAppdKUBgCllEpTGgCUUipNaQBQSqk0pQFAKaXSlAYA\npZRKUxoAlFIqTWkAUEqpNKUBQCml0pQGAKWUSlMaAJRSKk1pAFBKqTSlAUAppdKUBgCllEpTCQUA\nEckXkVdF5EN7OqKTdP9HRLaLyDYReVJEMhI5r1JKqcQlWgO4FXjdGDMVeN1ejiIi44BvASXGmNmA\nE7gswfOqZAkFwVcHoVCqc6KU6meuBPdfBiyx5x8F1gG3dHKeTBFpAbKATxM8b/oxBoJ+8DeAv96e\nts43drI+1ny75UCTdfxh42DOcph7GYyamdrvqpTqF4kGgFHGmAP2/EFgVPsExpj9IrIS2As0AX8z\nxvytswOKyPXA9QATJ05MMHspEgpBS6xCuYuCuaWh+3ShQPx5cGWCJ9v+5LTN54y0l7Patrky4JMN\nsOE+ePNXMHqOFQjmLIfc0X33OymlUkqMMV0nEHkNiFUK/AB41BgzPCLtYWNMVD+A3S/wR+BS4Ajw\nDPCsMebx7jJXUlJiNm3a1O2XSEjA3/OCuNOCvbHtGPESR3QB3b7A7rDcbt6dFXsfh7Pnv0V9JWz/\nE/zrKfj0PStvU06FuZfCjPOs4yqlBjQR2WyMKYknbbc1AGPM6V2c6JCIjDHGHBCRMUBFjGSnAx8b\nYyrtff4EnAB0GwB67Y2fW+3a8TSDhFriP64rI3ZBnF1kTWMWxt3Mu7wg0mc/RY/kFMHxX7M+laWw\ndTVsfRqeux5ezIYZX4R5l8LkU3oXYJRSA0qiTUAvAFcBd9nTNTHS7AUWi0gWVhPQUqBvL+vf/g2Y\nUMer6KwCGD4xjivuGOvd2eBM9OcaRIqmwdLb4NQfwN63rGCw/XnY+hTkjLaah+ZdZjUXKaUGpW6b\ngLrcWaQAeBqYCHwCXGKMqRGRscBDxphz7HR3YjUBBYD3gf9ljPF1d/xeNwEZM3CuqoeSlmYo/asV\nDD78m9UnMXKWVSuY8yUYNjbVOVQq7fWkCSihANDX+qUPQPVOQ7XVX7B1NZS/CwhM/rxVK5jxRfDm\npjqHSqUlDQCqf1V/ZPcXrIbDZdYdSDPOszqPp5yaXk1nSqWYBgCVGsbAvo1WP8G2P0HzEcgeaT9f\ncCmMmadNc0r1MQ0AKvUCPquf4F9PQekr1t1WRdNh7iUw5xIYPiHVOVRqSNIAoAaWxhrY8Tz8azXs\nexsQmHSSVSuYuQwyhqU6h0oNGRoA1MBV8zF88IxVM6j5yHq2ovgcKxgcsxSc7lTnUKlBTQOAGviM\ngf2brUCw7Y/QVANZhTD7Yuu20rHHan+BUr2gAUANLgE/7HnNuoto918g6IOCqVatYO4lMOKoVOdQ\nqUFDA4AavJqOwI411hAUn6y31k08waoVzFwGmTFfOaGUsmkAUEPDkb1WINi6GqpKwemBaWdZD5sd\ncwa4PKnOoVIDjgYANbQYA5++bwWCD56FxirIzIfZF1nDVo8v0f4CpWwaANTQFWyBj96wHjbb9RIE\nmiF/Slt/Qf6UVOdQqZTSAKDSQ3Mt7HzBupOobD1gYMLxViCYdRFk5ac6h0r1Ow0AKv18Vm4/X7Aa\nKneCww3TzrRqBtPOtN67oFQa0ACg0pcxcHCr1Xn8wTNQfwgyhsOsC61gMHGx9heoIU0DgFIAwQB8\nvM6qFex60XpP8/CjrEAw7zIoODrVOVQq6TQAKNWer94KAv96Cj7+u/XGuHElVjCYfTFkF6Q6h0ol\nhQYApbpSe8BqHtq6Gg5tA4fLeq5g3qUw7WxwZ6Q6h0r1mgYApeJ1cJv9fMEzUHcAvMOsJ47nXWY9\ngexwpDqHSvWIBgCleioUhI//YQWDHS9ASwPkTYS5X7IeNiualuocqoEqFLT6l1qaYkxjrWu3zd/Y\ncZ03F65+sVfZ0QCgVCL8DbDrZeths4/WWv0FY+ZbtYLZyyGnKNU5VPEwxnoxUU8K47jWNUSvC/p7\nnjdxgicb3Jn2Jyt6ml0EFzzQq6+tAUCpZKk7BNuetTqPD261/uMesxTGLwRxgMNpTaM+TutW08h1\nMdPF+ITTSbvjtU8Xa//IdJKE/PXh7bKhYCeFbGcFdG8K6kYrePeUq32hHKOAjntdFnhirOvD915o\nAFCqL1TstJqItj4DteWpzk0/kBiBp5cBKlzgt141+3qRnW6umhNaZx/XlTHo+300ACjVl4yBUMC6\numz9hIIRy8aeBqPThNPGWGdi7B+KtX8w4vixzt26f4x9w+lMF+e2tyf73OKwC9s4r5pjbXO69SG+\nOPQkALgSPNGXgDuAGcAiY0zM0lpEzgJ+BTiBh4wxdyVyXqVSSkRfXamGhETrOtuAi4B/dJZARJzA\n/cDZwEzgyyIyM8HzKqWUSlBCNQBjzE4A6bpatgjYY4z5t532KWAZsCORcyullEpMf/R2jAP2RSyX\n2+tiEpHrRWSTiGyqrKzs88wppVS66rYGICKvAaNjbPqBMWZNsjNkjHkQeBCsTuBkH18ppZSl2wBg\njDk9wXPsByZELI+31ymllEqh/mgCeheYKiKTRcQDXAa80A/nVUop1YWEAoCIXCgi5cDngJdE5BV7\n/VgReRnAGBMAvgG8AuwEnjbGbE8s20oppRKV6F1AzwHPxVj/KXBOxPLLwMuJnEsppVRyDegngUWk\nEvikl7sXAlVJzE6yaL56RvPVM5qvnhmK+TrKGBPXiIUDOgAkQkQ2xfs4dH/SfPWM5qtnNF89k+75\nGtyjHimllOo1DQBKKZWmhnIAeDDVGeiE5qtnNF89o/nqmbTO15DtA1BKKdW1oVwDUEop1QUNAEop\nlaYGXQAQkbNEZLeI7BGRW2NsFxH5tb19q4gcG+++KcxXmYh8ICJbRCSpr0CLI1/TReQtEfGJyM09\n2TeF+Url73W5/e/3gYhsEJF58e6bwnz12e8VZ96W2XnbYo/0e1K8+6YwXyn7G4tIt1BEAiKyvKf7\nxs0YM2g+WG8U+wiYAniAfwEz26U5B/gLIMBi4J14901FvuxtZUBhin6vkcBC4KfAzT3ZNxX5GgC/\n1wnACHv+7AH09xUzX335e/Ugbzm09TfOBXYNkN8sZr5S/TcWkW4t1ggKy/vq9xpsNYDwy2WMMX6g\n9eUykZYBjxnL28BwERkT576pyFdf6jZfxpgKY8y7QEtP901RvvpSPPnaYIw5bC++jTW6bVz7pihf\nfS2evNUbuwQDsgET774pyldfivc7fxP4I1DRi33jNtgCQDwvl+ksTY9eTNOP+QLrD+81EdksItcn\nKU/x5qsv9u3rYw+U3+s6rFpdb/btr3xB3/1ecedNrIEjdwEvAdf2ZN8U5AtS+DcmIuOAC4Hf9HTf\nnkpoMDiVNCcZY/aLyEjgVRHZZYzp9D3LKvW/l4icilXQntRd2v7USb5S/nsZe+BIEfk88J9Aou8Z\nSYou8pXK3+yXwC3GmJB0/brdhA22GkA8L5fpLE1fvpgmkXxhjGmdVmCNrrqoH/PVF/v26bFT/XuJ\nyFzgIWCZMaa6J/umIF99+XvFnbeIvPwDmCIihT3dtx/zleq/sRLgKREpA5YDD4jIBXHu2zPJ7uTo\nyw9WjeXfwGTaOkFmtUtzLtGdrRvj3TdF+coGciPmNwBn9Ve+ItLeQXQncEp/ry7yldLfC5gI7AFO\n6O136ud89dnv1YO8HUNbZ+uxWIWWDIDfrLN8DYj/k3b6VbR1Aif990rKH0F/frDupinF6g3/gb1u\nBbDCnhfgfnv7B0BJV/umOl9YPfr/sj/bU5Cv0VhtibXAEXt+2AD4vWLmawD8Xg8Bh4Et9mfTAPn7\nipmvvv694szbLfa5twBvYTWvDITfLGa+Uv031i7tKuwA0Be/lw4FoZRSaWqw9QEopZRKEg0ASimV\npjQAKKVUmtIAoJRSaUoDgFJKpSkNAEoplaY0ACilVJr6/1iR7gTCwsGKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c86cdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r_list,r_put_OTM_df[\"delta\"],label=\"put option, OTM\")\n",
    "plt.plot(r_list,r_put_ITM_df[\"delta\"],label=\"put option, ITM\")\n",
    "plt.plot(r_list,r_put_OTM_df[\"BS delta\"],label=\"European put option, OTM\")\n",
    "plt.plot(r_list,r_put_ITM_df[\"BS delta\"],label=\"European put option, ITM\")\n",
    "plt.legend()\n",
    "plt.title(\"r vs. delta\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price: 0.16549639179822845, delta-hedge: -0.6004957853402437\n",
      "price: 0.03146826661884927, delta-hedge: -0.3235174029320515\n",
      "price: 0.270610451533873, delta-hedge: -1.1519958153121161\n",
      "price: 0.08051023635768553, delta-hedge: -0.4453606826326743\n",
      "price: 0.3468164480115119, delta-hedge: -1.1418417080003858\n",
      "price: 0.16586474492507447, delta-hedge: -0.9207261925386652\n",
      "price: 0.4385731231050367, delta-hedge: -1.3690636958003932\n",
      "price: 0.23741869826842646, delta-hedge: -0.4459964462449415\n",
      "price: 0.5271879533910762, delta-hedge: -1.222139944434461\n",
      "price: 0.3309009406739315, delta-hedge: -0.8195401248074271\n"
     ]
    }
   ],
   "source": [
    "r_df1,r_df2 = averageExerciseTimeRiskFreeRate(S0=stock_price,K1=K1,K2=K2,T=time_to_maturity,r_list=r_list,q=dividend,sigma=volatility,option_type=\"c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r_call_ITM_df = r_df1\n",
    "r_call_OTM_df = r_df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wr46G4fMZdh6uZmOx1Uf/tz2VnKzzADCiXzdu/8YgLh2SysVZvUhJjHM0VqUiiSb+aORe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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d094eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r_list,r_call_OTM_df[\"average exercise time\"],label=\"call option, OTM\")\n",
    "plt.plot(r_list,r_call_ITM_df[\"average exercise time\"],label=\"call option, ITM\")\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"r vs. average exercise time\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZF4dwdbVypLZPJXdFuRjNJ2HTclj/OjRWw+BJ2r6kw9LV3JdL1HEzi/qsTIwH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\nSilVhTTclVKqCmm4K6VUFdJwV0qpKvR/rOsXRmQ3PUMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cc236d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r_list,r_call_OTM_df[\"price\"],label=\"call option, OTM\")\n",
    "plt.plot(r_list,r_call_ITM_df[\"price\"],label=\"call option, ITM\")\n",
    "plt.plot(r_list,r_call_OTM_df[\"BS price\"],label=\"European call option, OTM\")\n",
    "plt.plot(r_list,r_call_ITM_df[\"BS price\"],label=\"European call option, ITM\")\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"r vs. price\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vSv72pDclf3tr8eLF3HHHHXz00UeuipnB5kDGJkSQX95AfnkDo+PCiAwx9+nr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\nxd1xHKeG/AXLEGGjTGbSkwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cdbe518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r_list,r_call_OTM_df[\"delta\"],label=\"call option, OTM\")\n",
    "plt.plot(r_list,r_call_ITM_df[\"delta\"],label=\"call option, ITM\")\n",
    "plt.plot(r_list,r_call_OTM_df[\"BS delta\"],label=\"European call option, OTM\")\n",
    "plt.plot(r_list,r_call_ITM_df[\"BS delta\"],label=\"European call option, ITM\")\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"r vs. delta\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2 dividend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "q_low=0\n",
    "q_high=0.3\n",
    "q_list = [0.1*i for i in range(3)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price: 0.06369406627041597, delta-hedge: 0.3979475103779342\n",
      "price: 0.23384361558768862, delta-hedge: 0.8038041002619591\n",
      "price: 0.07278907815432188, delta-hedge: 0.3804692543538679\n",
      "price: 0.2825511765834884, delta-hedge: 0.5916889430542438\n",
      "price: 0.12117480061242318, delta-hedge: 0.36361468136140496\n",
      "price: 0.36870448059543726, delta-hedge: 0.8385521966915168\n"
     ]
    }
   ],
   "source": [
    "q_df1,q_df2 = averageExerciseTimeDividend(S0=stock_price,K1=K1,K2=K2,T=time_to_maturity,r=risk_free_rate,q_list=q_list,sigma=volatility,option_type=\"p\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "q_put_OTM_df = q_df1\n",
    "q_put_ITM_df = q_df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dividend</th>\n",
       "      <th>price</th>\n",
       "      <th>BS price</th>\n",
       "      <th>delta</th>\n",
       "      <th>average exercise time</th>\n",
       "      <th>BS delta</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.063694</td>\n",
       "      <td>0.050097</td>\n",
       "      <td>-0.397948</td>\n",
       "      <td>0.950875</td>\n",
       "      <td>0.049991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.072789</td>\n",
       "      <td>0.078301</td>\n",
       "      <td>-0.380469</td>\n",
       "      <td>0.954250</td>\n",
       "      <td>0.079694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.121175</td>\n",
       "      <td>0.114427</td>\n",
       "      <td>-0.363615</td>\n",
       "      <td>0.990250</td>\n",
       "      <td>0.113926</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   dividend     price  BS price     delta  average exercise time  BS delta\n",
       "0       0.0  0.063694  0.050097 -0.397948               0.950875  0.049991\n",
       "1       0.1  0.072789  0.078301 -0.380469               0.954250  0.079694\n",
       "2       0.2  0.121175  0.114427 -0.363615               0.990250  0.113926"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_put_OTM_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dividend</th>\n",
       "      <th>price</th>\n",
       "      <th>BS price</th>\n",
       "      <th>delta</th>\n",
       "      <th>average exercise time</th>\n",
       "      <th>BS delta</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.233844</td>\n",
       "      <td>0.202370</td>\n",
       "      <td>-0.803804</td>\n",
       "      <td>0.662250</td>\n",
       "      <td>0.203310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.282551</td>\n",
       "      <td>0.265429</td>\n",
       "      <td>-0.591689</td>\n",
       "      <td>0.913625</td>\n",
       "      <td>0.264599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.368704</td>\n",
       "      <td>0.332059</td>\n",
       "      <td>-0.838552</td>\n",
       "      <td>0.939000</td>\n",
       "      <td>0.331158</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   dividend     price  BS price     delta  average exercise time  BS delta\n",
       "0       0.0  0.233844  0.202370 -0.803804               0.662250  0.203310\n",
       "1       0.1  0.282551  0.265429 -0.591689               0.913625  0.264599\n",
       "2       0.2  0.368704  0.332059 -0.838552               0.939000  0.331158"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_put_ITM_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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o379/o4q4Y5wOH4iI1KdNHG3WAP0invcNp1Vz9w3ufoG7FwHnAQXA8nDemvD7Z8AsgqGj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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cc53198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(q_list,q_put_OTM_df[\"average exercise time\"],label=\"put option, OTM\")\n",
    "plt.plot(q_list,q_put_ITM_df[\"average exercise time\"],label=\"put option, ITM\")\n",
    "plt.legend()\n",
    "plt.title(\"q vs. average exercise time\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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atWoVxcXFPPPMM0Pq8RYvXtzpB8J95ZlnniE7O5srr7yy3x6jK1qW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\nhNHgV0qpCPP/AHUtNQn4ld02AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cc53b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(q_list,q_put_OTM_df[\"price\"],label=\"put option, OTM\")\n",
    "plt.plot(q_list,q_put_ITM_df[\"price\"],label=\"put option, ITM\")\n",
    "plt.plot(q_list,q_put_OTM_df[\"BS price\"],label=\"European put option, OTM\")\n",
    "plt.plot(q_list,q_put_ITM_df[\"BS price\"],label=\"European put option, ITM\")\n",
    "plt.legend()\n",
    "plt.title(\"q vs. price\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RztLf/ZIJY0ez8M6H+Lx8G5vKytld8U3jcNALZnT4cNAtEpfV/CNuzr/oUp5+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\nTAdOtl8/AqwiIgGEHCdTROq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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d051668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(q_list,q_put_OTM_df[\"delta\"],label=\"put option, OTM\")\n",
    "plt.plot(q_list,q_put_ITM_df[\"delta\"],label=\"put option, ITM\")\n",
    "plt.plot(q_list,q_put_OTM_df[\"BS delta\"],label=\"European put option, OTM\")\n",
    "plt.plot(q_list,q_put_ITM_df[\"BS delta\"],label=\"European put option, ITM\")\n",
    "plt.legend()\n",
    "plt.title(\"q vs. delta\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price: 0.20992494280967952, delta-hedge: -0.5291048150527156\n",
      "price: 0.07833748403676652, delta-hedge: -0.5117878830988531\n",
      "price: 0.14328186003546795, delta-hedge: -0.8411543566665243\n",
      "price: 0.04513553628381123, delta-hedge: -0.32505839980808715\n",
      "price: 0.11701486198534565, delta-hedge: -0.6914820060517288\n",
      "price: 0.023962024608411098, delta-hedge: -0.21388854758531903\n"
     ]
    }
   ],
   "source": [
    "q_df1,q_df2 = averageExerciseTimeDividend(S0=stock_price,K1=K1,K2=K2,T=time_to_maturity,r=risk_free_rate,q_list=q_list,sigma=volatility,option_type=\"c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "q_call_ITM_df = q_df1\n",
    "q_call_OTM_df = q_df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dividend</th>\n",
       "      <th>price</th>\n",
       "      <th>BS price</th>\n",
       "      <th>delta</th>\n",
       "      <th>average exercise time</th>\n",
       "      <th>BS delta</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.209925</td>\n",
       "      <td>0.202509</td>\n",
       "      <td>0.529105</td>\n",
       "      <td>0.876250</td>\n",
       "      <td>0.201440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.143282</td>\n",
       "      <td>0.135550</td>\n",
       "      <td>0.841154</td>\n",
       "      <td>0.864250</td>\n",
       "      <td>0.135886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.117015</td>\n",
       "      <td>0.085570</td>\n",
       "      <td>0.691482</td>\n",
       "      <td>0.541125</td>\n",
       "      <td>0.086834</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   dividend     price  BS price     delta  average exercise time  BS delta\n",
       "0       0.0  0.209925  0.202509  0.529105               0.876250  0.201440\n",
       "1       0.1  0.143282  0.135550  0.841154               0.864250  0.135886\n",
       "2       0.2  0.117015  0.085570  0.691482               0.541125  0.086834"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_call_ITM_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dividend</th>\n",
       "      <th>price</th>\n",
       "      <th>BS price</th>\n",
       "      <th>delta</th>\n",
       "      <th>average exercise time</th>\n",
       "      <th>BS delta</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.078337</td>\n",
       "      <td>0.072253</td>\n",
       "      <td>0.511788</td>\n",
       "      <td>0.98250</td>\n",
       "      <td>0.071853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.045136</td>\n",
       "      <td>0.040149</td>\n",
       "      <td>0.325058</td>\n",
       "      <td>0.97600</td>\n",
       "      <td>0.040766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.023962</td>\n",
       "      <td>0.020673</td>\n",
       "      <td>0.213889</td>\n",
       "      <td>0.94825</td>\n",
       "      <td>0.020734</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   dividend     price  BS price     delta  average exercise time  BS delta\n",
       "0       0.0  0.078337  0.072253  0.511788                0.98250  0.071853\n",
       "1       0.1  0.045136  0.040149  0.325058                0.97600  0.040766\n",
       "2       0.2  0.023962  0.020673  0.213889                0.94825  0.020734"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_call_OTM_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OHilh58Gjny07bLpztft+SQE7kfhTKzmbqPyM4+SKJz284ihXPtUblxIMELqpWEQSSYNL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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cf0fb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(q_list,q_call_ITM_df[\"average exercise time\"],label=\"call option, ITM\")\n",
    "plt.plot(q_list,q_call_OTM_df[\"average exercise time\"],label=\"call option, OTM\")\n",
    "plt.legend()\n",
    "plt.title(\"q vs. average exercise time\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hwoWN3YU6s2WE4AQkYawBnAZ2A3dprX+15F/NCGElsEFrvdTquRCtdbrl5/+H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\nCYJhGIYBmCAYhmEYnv8Hxr/GmwfBxl4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cf4fa20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(q_list,q_call_ITM_df[\"price\"],label=\"call option, ITM\")\n",
    "plt.plot(q_list,q_call_OTM_df[\"price\"],label=\"call option, OTM\")\n",
    "plt.plot(q_list,q_call_OTM_df[\"BS price\"],label=\"European call option, ITM\")\n",
    "plt.plot(q_list,q_call_ITM_df[\"BS price\"],label=\"European call option, OTM\")\n",
    "plt.legend()\n",
    "plt.title(\"q vs. price\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Fh7qEM+VvqGIx5e/f//53TjrpJBYsWABAYmIiDz/8cEhnXCeffDLr16+nra2N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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c77cf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(q_list,q_call_ITM_df[\"delta\"],label=\"call option, ITM\")\n",
    "plt.plot(q_list,q_call_OTM_df[\"delta\"],label=\"call option, OTM\")\n",
    "plt.plot(q_list,q_call_ITM_df[\"BS delta\"],label=\"European call option, ITM\")\n",
    "plt.plot(q_list,q_call_OTM_df[\"BS delta\"],label=\"European call option, OTM\")\n",
    "plt.legend()\n",
    "plt.title(\"q vs. delta\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.3 volatility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sigma_low = 0.3\n",
    "sigma_high = 0.6\n",
    "sigma_list = [0.3, 0.4, 0.5, 0.6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price: 0.05744485878780141, delta-hedge: 0.278073757833854\n",
      "price: 0.22042752123264014, delta-hedge: 0.7675779308893705\n",
      "price: 0.10191951843712066, delta-hedge: 0.4400875854718613\n",
      "price: 0.2452901883686492, delta-hedge: 0.642588034338732\n",
      "price: 0.10916136399515046, delta-hedge: 0.27002551251377127\n",
      "price: 0.30912445467322314, delta-hedge: 0.5117862781937207\n",
      "price: 0.16053806012604524, delta-hedge: 0.29891383083442263\n",
      "price: 0.32523690546655193, delta-hedge: 0.42211719182261265\n"
     ]
    }
   ],
   "source": [
    "sigma_df1,sigma_df2 = averageExerciseTimeVolatility(S0=stock_price,K1=K1,K2=K2,T=time_to_maturity,r=risk_free_rate,q=dividend,sigma_list=sigma_list,option_type=\"p\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sigma_put_OTM_df = sigma_df1\n",
    "sigma_put_ITM_df = sigma_df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BHh6fU9xptZlBdTVPQ5c1xu9UlTey9vDQq+vZW1TCtaNTuXPSQNrGtvF31ozx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\nHrovKdh/o0cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c85bf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sigma_list,sigma_put_ITM_df[\"average exercise time\"],label=\"put option, ITM\")\n",
    "plt.plot(sigma_list,sigma_put_OTM_df[\"average exercise time\"],label=\"put option, OTM\")\n",
    "plt.legend()\n",
    "plt.title(\"sigma vs. average exercise time\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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g3GJmbkYiC7KTuWxMDGbTxfW4T9hPsKHydDmEihZjQjspNImi5CJvOYRhloHx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\nnGsx/wcg3wrSQqysVgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c8f4160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sigma_list,sigma_put_ITM_df[\"price\"],label=\"put option, ITM\")\n",
    "plt.plot(sigma_list,sigma_put_OTM_df[\"price\"],label=\"put option, OTM\")\n",
    "plt.plot(sigma_list,sigma_put_ITM_df[\"BS price\"],label=\"European put option, ITM\")\n",
    "plt.plot(sigma_list,sigma_put_OTM_df[\"BS price\"],label=\"European put option, OTM\")\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"sigma vs. price\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5mgD6wKpVq3jvvfd6ZF/l5eU88cQT0eWysjJ+8pOf9Mi+Y82ZM4eysjJmz57N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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c74e1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sigma_list,sigma_put_ITM_df[\"delta\"],label=\"put option, ITM\")\n",
    "plt.plot(sigma_list,sigma_put_OTM_df[\"delta\"],label=\"put option, OTM\")\n",
    "plt.plot(sigma_list,sigma_put_ITM_df[\"BS delta\"],label=\"European put option, ITM\")\n",
    "plt.plot(sigma_list,sigma_put_OTM_df[\"BS delta\"],label=\"European put option, OTM\")\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"sigma vs. delta\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price: 0.20688963624406514, delta-hedge: -0.6166552181599961\n",
      "price: 0.07740253314872338, delta-hedge: -0.4329936547852073\n",
      "price: 0.25337734978682314, delta-hedge: -0.9248152664575845\n",
      "price: 0.12665229141843717, delta-hedge: -0.34575457681613114\n",
      "price: 0.2678658244179845, delta-hedge: -0.7311824586438068\n",
      "price: 0.18493295263470091, delta-hedge: -0.815996875222987\n",
      "price: 0.18013985936035184, delta-hedge: -1.0739456483533256\n",
      "price: 0.19798550930741426, delta-hedge: -0.7692272493477635\n"
     ]
    }
   ],
   "source": [
    "sigma_df1,sigma_df2 = averageExerciseTimeVolatility(S0=stock_price,K1=K1,K2=K2,T=time_to_maturity,r=risk_free_rate,q=dividend,sigma_list=sigma_list,option_type=\"c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sigma_call_ITM_df = sigma_df1\n",
    "sigma_call_OTM_df = sigma_df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SSlm6x0Vyw4WZfL6jkI+2adduc1pM7saYamABsAzYDPzdGLNRROaLyHyvot8C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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c727160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sigma_list,sigma_call_ITM_df[\"average exercise time\"],label=\"call option, ITM\")\n",
    "plt.plot(sigma_list,sigma_call_OTM_df[\"average exercise time\"],label=\"call option, OTM\")\n",
    "plt.legend()\n",
    "plt.title(\"sigma vs. average exercise time\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HuPPtjewqtnLbBf25f9YQ3KXrp9M6m+CX4ZyiS6ltsDsD/XiYN6/aS6z1NK9lTAoiAo0w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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c72f518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sigma_list,sigma_call_ITM_df[\"price\"],label=\"call option, ITM\")\n",
    "plt.plot(sigma_list,sigma_call_OTM_df[\"price\"],label=\"call option, OTM\")\n",
    "plt.plot(sigma_list,sigma_call_ITM_df[\"BS price\"],label=\"European call option, ITM\")\n",
    "plt.plot(sigma_list,sigma_call_OTM_df[\"BS price\"],label=\"European call option, OTM\")\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"sigma vs. price\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3Q7B2IQw6GS58oW01dZsdknpbP148tfUDdbV1YiPqfxCU5h5529dvBN4fBE19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\ndIuUCmmhF+4N2WOsQOg9rv7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AsSkpdaWPRkZ76BSoSqlwEXLhbktKInr48EYPHnoHtl5U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\nlVIqDGm4K6VUGNJwV0qpMPT/AesqbKWfkGWqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cef0710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sigma_list,sigma_call_ITM_df[\"delta\"],label=\"call option, ITM\")\n",
    "plt.plot(sigma_list,sigma_call_OTM_df[\"delta\"],label=\"call option, OTM\")\n",
    "plt.plot(sigma_list,sigma_call_ITM_df[\"BS delta\"],label=\"European call option, ITM\")\n",
    "plt.plot(sigma_list,sigma_call_OTM_df[\"BS delta\"],label=\"European call option, OTM\")\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"sigma vs. delta\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}