{ "cells": [ { "cell_type": "markdown", "id": "e9e1443d", "metadata": {}, "source": [ "# European option pricing with ```pyop3``` continued\n", "\n", "Author: Caden Lee (caden.finsinyur@gmail.com)" ] }, { "cell_type": "code", "execution_count": 1, "id": "503fd439", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pyop3\n", "import matplotlib.pyplot as plt\n", "import scipy\n", "from scipy import stats" ] }, { "cell_type": "markdown", "id": "b5d3141e", "metadata": {}, "source": [ "## Overview\n", "In the previous tutorial, we explored quite broadly the use of ```pyop3``` library in pricing European options, starting with setting up the underlying asset lattice by creating the ```pyop3.binomial_tree``` object. Once the underlying asset lattice is initiated, we could visualize the tree by using the ```pyop3.tree_planter.show_tree()``` function.\n", "\n", "We then proceeded with pricing the European options. In that example, we explored pricing of European options on:\n", "- non-dividend paying underlying asset (given a. time-to-expiry, and b. spot date and expiry date)\n", "- Dividend paying underlying asset (known dollar dividends with ex-div coinciding expiry)\n", "- Dividend paying underlying asset (knwon dollar dividends with ex-div before expiry)\n", "- Underlying asset with known (dividend) yield\n", "\n", "In this tutorial, we will be demonstrating an alternative method to deriving call and put prices, which is faster than the method shown in the past tutorial. We will also be exploring the difference between the CRR tree and the RB tree. Thereafter, we will be comparing the numerical results of the two trees to the analytical solutions from the Black-Scholes option pricing model." ] }, { "cell_type": "markdown", "id": "67ed7e02", "metadata": {}, "source": [ "## Section 1: Faster implementation to calculate European call and put option values\n", "\n", "In tutorial 1, we demonstrated how we can derive the call option value and option tree using the ```call()``` method of the ```pyop3.european_option``` object. This methodology sets the foundation for pricing of more advanced options, such as the American options. However, this method is not essential for pricing of European options as European option does not require evaluation of every nodes in each time step. In fact, we can easily calculate the call option value by simply working on the terminal option pay off, by\n", "\n", "$$V_{call} = e^{-rT}\\sum_{i = 0}^N \\big(S_0(u)^{N-i}(d)^i - K\\big)\\times p^{N-i}(1-p)^i \\times \\bigg(\\begin{matrix} N\\\\ i \\end{matrix}\\bigg)$$\n", "\n", "where \n", "- $S_0$ is the spot price at time 0, \n", "- $K$ is the option strike price, \n", "- $e^{-rT}$ is the discount factor,\n", "- $N$ is the number of time step, \n", "- $u$ is the upward multiplier, \n", "- $d$ is the downward multiplier, \n", "- $p$ is the risk-neutral probability of an upward movement in underlying price, and \n", "- $\\bigg(\\begin{matrix} N\\\\ i \\end{matrix}\\bigg)$ means \"N choose i\", which refers to the frequency of occurance of the node i at expiration\n", "\n", "Once the call option value is determined, one can easily find the put option value using the put-call parity\n", "\n", "$$C + Ke^{-rT} = P + S_0$$\n", "\n", "Where\n", "- $C$ is the call option value, and\n", "- $P$ is the put option value\n", "\n", "The fast implementation can be done by calling the ```fast_put_call()``` method of the ```pyop3.european_option``` object. Below shows the difference in execution time." ] }, { "cell_type": "code", "execution_count": 2, "id": "efe866da", "metadata": {}, "outputs": [], "source": [ "S0 = 300\n", "r = 0.08\n", "sigma = 0.3\n", "T = 0.333\n", "\n", "asset = pyop3.binomial_tree(S0, r, T, sigma = sigma, N = 50)\n", "asset_options_1 = pyop3.european_option(asset, 300)\n", "asset_options_2 = pyop3.european_option(asset.copy(), 300)" ] }, { "cell_type": "code", "execution_count": 3, "id": "b1c7481e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "880 µs ± 175 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" ] } ], "source": [ "%%timeit\n", "\n", "# Initialize the binomial tree object\n", "asset_options_1.call()\n", "asset_options_1.put()\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "203e63d4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "call: 24.502361910452436\n", "put: 16.61587630625242\n" ] } ], "source": [ "print('call: ', asset_options_1.call_value)\n", "print('put: ', asset_options_1.put_value)" ] }, { "cell_type": "code", "execution_count": 5, "id": "0c4a0e26", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "199 µs ± 15.3 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" ] } ], "source": [ "%%timeit\n", "\n", "asset_options_2.fast_put_call()" ] }, { "cell_type": "code", "execution_count": 6, "id": "370e0c08", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "call: 24.502361910452432\n", "put: 16.615876306250755\n" ] } ], "source": [ "print('call: ', asset_options_2.call_value)\n", "print('put: ', asset_options_2.put_value)" ] }, { "cell_type": "markdown", "id": "f8c689e3", "metadata": {}, "source": [ "The fast implementation takes roughly 20% of the required time compared to running ```call()``` and ```put()``` methods separately." ] }, { "cell_type": "markdown", "id": "5328dff6", "metadata": {}, "source": [ "## Section 2: CRR vs RB Trees\n", "\n", "The binomial tree option pricing algorithm first introduced by Cox et al in their 1979 paper \"Option Pricing: A Simplified Approach\". This simplistic and elegant approach to option pricing offers the community an alternative to the Black-Scholes model, which is daunting to some in its mathematics.\n", "\n", "The binomial option pricing algorithm generally works as it ensures weak convergence of stochatic processes and matches the first two moments of the log-returns.\n", "\n", "The Cox-Ross-Rubinstein (CRR) Tree suggests a binomial model in which the price of the underlying asset can, at each point in time, move up by a factor of $u$ and down by a factor of $d$, which $d = \\frac{1}{u}$. With these parameters, the log-tree is such that it is symmetrical about the spot price at time 0. Relating to the Black-Scholes model, we find\n", "\n", "$$u = e^{\\sigma \\sqrt{T}}, d = e^{- \\sigma \\sqrt{T}}, p = \\frac{e^{r \\Delta t} - d}{u - d}$$\n", "\n", "In the same year, Rendleman and Bartter also provided their suggestions of the Binomial tree option pricing algorithm. It looks similar to that of the CRR tree, except that it restricts the risk-neutral probability to $p = 0.5$. This means that the log-tree is no longer symmetrical about the spot price at time 0.\n", "\n", "$$p = \\frac{1}{2}, u = e^{(r-0.5\\sigma^2)\\Delta t + \\sigma \\sqrt{\\Delta t}}, d = e^{(r-0.5\\sigma^2)\\Delta t - \\sigma \\sqrt{\\Delta t}}$$\n", "\n", "The RB tree has upward and downward movements similar to the discrete version of the Black-Schole model of asset price dynamic, which takes the form\n", "\n", "$$S_{t + \\Delta t} = S_0e^{(r - 0.5 \\sigma^2)\\Delta t + \\sigma (W_{t+\\Delta t} - W_t)}$$" ] }, { "cell_type": "code", "execution_count": 7, "id": "fd1d266a", "metadata": {}, "outputs": [], "source": [ "asset_CRR = pyop3.binomial_tree(S0, r, T, sigma = sigma)\n", "asset_RB = pyop3.binomial_tree(S0, r, T, sigma = sigma, tree_type= \"RB\")" ] }, { "cell_type": "code", "execution_count": 8, "id": "45e0057b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pyop3.tree_planter.show_tree(asset_CRR.underlying_asset_tree(), \"The Cox-Ross-Rubinstein Tree\")\n", "pyop3.tree_planter.show_tree(asset_RB.underlying_asset_tree(), \"The Rendleman and Bartter Tree\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "15fe6bd3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Call Option value based on CRR: $23.37\n", "Call Option value based on RB: $23.96\n" ] } ], "source": [ "asset_CRR_option = pyop3.european_option(asset_CRR,300)\n", "asset_CRR_option.fast_put_call()\n", "\n", "asset_RB_option = pyop3.european_option(asset_RB,300)\n", "asset_RB_option.fast_put_call()\n", "\n", "print('Call Option value based on CRR: ${:.2f}'.format(asset_CRR_option.call_value))\n", "print('Call Option value based on RB: ${:.2f}'.format(asset_RB_option.call_value))" ] }, { "cell_type": "markdown", "id": "525720ad", "metadata": {}, "source": [ "## Section 3: Comparison Binomial Tree Models vs Black-Scholes Model\n", "\n", "In this section, we shall evaluate the efficacy of the binomial tree option pricing model in approximating the analytical solution of option prices by the Black-Scholes model.\n", "\n", "The Option pricing equation based on the Black-Scholes model is as follows:\n", "\n", "$$V(0,S) = S_0\\Phi(d_1) - Ke^{-r(T)}\\Phi(d_2)$$\n", "\n", "where\n", "- $d_2 = \\frac{ln(\\frac{S_0}{K}) + (r - \\frac{1}{2}\\sigma^2)(T)}{\\sigma \\sqrt{T}}$\n", "- $d_1 = \\frac{ln(\\frac{S_0}{K}) + (r + \\frac{1}{2}\\sigma^2)(T)}{\\sigma \\sqrt{T}} = d_2 + \\sigma \\sqrt{T}$\n", "- $\\Phi(d_1) = \\int_{-\\infty}^{d_1} \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{1}{2}(z - \\sigma \\sqrt{T})^2} dz$ is the standard cumulative distribution function\n", "- $\\Phi(d_2) = \\int_{-\\infty}^{d_2} \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{1}{2}z^2} dz$ is the standard cumulative distribution function\n", "\n", "In the case of a vanilla put option, where $H(T,S) = max(K - S_T,0)$, the option pricing formula is:\n", "\n", "$$V(0,S) = Ke^{-r(T)}\\Phi(-d_2) - S_0\\Phi(-d_1)$$" ] }, { "cell_type": "code", "execution_count": 10, "id": "e399d549", "metadata": {}, "outputs": [], "source": [ "# Create function to price vanilla options analytically using Black-Scholes Model\n", "def black_scholes_option_pricer(S, K, r, T, sigma, call = True):\n", " '''\n", " Function calculates option prices based on Black-scholes model.\n", " Three modes available: Vanilla (default), Cash-or-Nothing (CON), Asset-or-Nothing (AON)\n", " \n", " Inputs:\n", " S: underlying asset price at t; can be an array of prices\n", " K: strike price; can be an array of prices\n", " r: interest rate, annualized\n", " T: time to expiration (also the T-t in our equations), in number of years\n", " sigma: implied volatility of the option\n", " call: default True. True if pricing call options; otherwise False\n", "\n", " Outputs:\n", " Option Prices.\n", " '''\n", "\n", " d2 = (np.log(S/K) +(r - 0.5*np.square(sigma))*(T))/(sigma*np.sqrt(T))\n", " d1 = d2 + sigma*np.sqrt(T)\n", " \n", " d2 = d2 if call == True else -d2\n", " d1 = d1 if call == True else -d1\n", " \n", " option_values = S*scipy.stats.norm.cdf(d1) - K*np.exp(-r*T)*scipy.stats.norm.cdf(d2)\n", " option_values = option_values if call == True else -option_values\n", "\n", " return option_values" ] }, { "cell_type": "code", "execution_count": 11, "id": "9498c73c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "238 µs ± 13.5 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" ] } ], "source": [ "%%timeit\n", "\n", "analytical_price = black_scholes_option_pricer(S0, 300, r, T, sigma)" ] }, { "cell_type": "code", "execution_count": 12, "id": "5ca8994e", "metadata": {}, "outputs": [], "source": [ "analytical_price = black_scholes_option_pricer(S0, 300, r, T, sigma)\n", "analytical_price_arr = np.ones(100) * analytical_price\n", "\n", "upp_limit = analytical_price_arr*1.005\n", "low_limit = analytical_price_arr*0.995\n", "\n", "x = np.arange(1,101,1)" ] }, { "cell_type": "markdown", "id": "2b568ea8", "metadata": {}, "source": [ "Now that we have initialized our analytical solution, we shall investigate the convergence of the binomial tree models to the analytical solution. Starting from N = 1, we shall increase the time step to N = 100 and derive all the option prices with each number of time steps. We then plot the array of option prices from CRR Tree and RB Tree, and plot them against the analytical solution respectively." ] }, { "cell_type": "code", "execution_count": 13, "id": "069efeed", "metadata": {}, "outputs": [], "source": [ "CRR_tree_prices = np.zeros(100)\n", "for n in x:\n", " asset = pyop3.binomial_tree(S0, r, T, sigma = sigma, N = int(n))\n", " option = pyop3.european_option(asset, 300)\n", " option.call()\n", " CRR_tree_prices[n-1] = option.call_value\n", " " ] }, { "cell_type": "code", "execution_count": 14, "id": "84410f4b", "metadata": {}, "outputs": [], "source": [ "RB_tree_prices = np.zeros(100)\n", "for n in x:\n", " asset = pyop3.binomial_tree(S0, r, T, sigma = sigma, N = int(n), tree_type= 'RB')\n", " option = pyop3.european_option(asset, 300)\n", " option.call()\n", " RB_tree_prices[n-1] = option.call_value" ] }, { "cell_type": "code", "execution_count": 15, "id": "ea797abe", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(2,2, figsize = (12,12))\n", "fig.suptitle('Comparing Binomial Tree Models vs Analytical Call Price')\n", "\n", "# Plot CRR Tree and RB Tree against the analytical solution, from N = 1 to N = 100\n", "ax[0,0].set_title('Comparing CRR Tree and BS Model for K = 300')\n", "ax[0,0].plot(x, analytical_price_arr, label = 'BS')\n", "ax[0,0].plot(x, upp_limit, label = '+50 bps', ls = '-.', c = 'r')\n", "ax[0,0].plot(x, low_limit, label = '-50 bps', ls = '-.', c = 'r')\n", "ax[0,0].plot(x, CRR_tree_prices, label = 'CRR')\n", "ax[0,0].legend()\n", "\n", "ax[0,1].set_title('Comparing RB Tree and BS Model for K = 350')\n", "ax[0,1].plot(x, analytical_price_arr, label = 'BS')\n", "ax[0,1].plot(x, upp_limit, label = '+50 bps', ls = '-.', c = 'r')\n", "ax[0,1].plot(x, low_limit, label = '-50 bps', ls = '-.', c = 'r')\n", "ax[0,1].plot(x, RB_tree_prices, label = 'RB')\n", "ax[0,1].sharey(ax[0,0])\n", "ax[0,1].legend()\n", "\n", "# Plot CRR Tree and RB Tree against the analytical solution, for the last ten iterations\n", "\n", "ax[1,0].set_title('CRR Tree vs BS Model for K = 300, last 10 steps')\n", "ax[1,0].plot(x[-10:], analytical_price_arr[-10:], label = 'BS')\n", "ax[1,0].plot(x[-10:], upp_limit[-10:], label = '+50 bps', ls = '-.', c = 'r')\n", "ax[1,0].plot(x[-10:], low_limit[-10:], label = '-50 bps', ls = '-.', c = 'r')\n", "ax[1,0].plot(x[-10:], CRR_tree_prices[-10:], label = 'CRR')\n", "ax[1,0].legend()\n", "\n", "ax[1,1].set_title('RB Tree vs BS Model for K = 350, last 10 steps')\n", "ax[1,1].plot(x[-10:], analytical_price_arr[-10:], label = 'BS')\n", "ax[1,1].plot(x[-10:], upp_limit[-10:], label = '+50 bps', ls = '-.', c = 'r')\n", "ax[1,1].plot(x[-10:], low_limit[-10:], label = '-50 bps', ls = '-.', c = 'r')\n", "ax[1,1].plot(x[-10:], RB_tree_prices[-10:], label = 'RB')\n", "ax[1,1].legend()\n", "\n", "\n", "for chart in ax.flat:\n", " chart.set(xlabel='Number of time step N', ylabel='Call Option Price')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 16, "id": "55c235ac", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56,\n", " 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73,\n", " 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90,\n", " 91, 92, 93, 94, 95, 96, 97, 98, 99], dtype=int64),)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.where(np.abs(CRR_tree_prices - analytical_price) < analytical_price*0.005)" ] }, { "cell_type": "code", "execution_count": 17, "id": "6d53a9ea", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33, 34, 35, 36,\n", " 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,\n", " 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,\n", " 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,\n", " 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99], dtype=int64),)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.where(np.abs(RB_tree_prices - analytical_price) < analytical_price*0.005)" ] }, { "cell_type": "markdown", "id": "fbb60923", "metadata": {}, "source": [ "From the above results, we observed the following:\n", "1. Results from both CRR Tree and RB Tree converges to the analytical price asymptotically\n", "2. While the results converges, the convergence is not smooth and is accompanied by oscillations\n", "3. For At-the-money (ATM) call options, while the results from CRR tree converges, it oscillates between prices above and below the analytical solution\n", "4. For ATM call options, similar to the CRR Tree the results of RB tree converges; however it oscillates above the analytical price, albeit with less range\n", "5. For ATM call options, the RB Tree converges to within 50 bps of the analytical price earlier than the CRR Tree\n", "\n", "Results for In-the-money (ITM) and Out-of-the-money (OTM) calls may arrive at different conclusions, but all exhibit convergence with oscillations." ] }, { "cell_type": "markdown", "id": "09bbdedd", "metadata": {}, "source": [ "## Section 4: Comparing Binomial models to Analytical Solution across strikes\n", "\n", "Now that we are comfortable with the convergence, we shall compare the results across strikes. In order to accomodate all strike levels, we set a conservative number of steps of N = 100 to ensure that our results do converge well." ] }, { "cell_type": "code", "execution_count": 18, "id": "ef7c388e", "metadata": {}, "outputs": [], "source": [ "strikes = np.arange(100,501,1)\n", "analytical_price_per_strike = black_scholes_option_pricer(S0, strikes, r, T, sigma)" ] }, { "cell_type": "code", "execution_count": 19, "id": "43a6a057", "metadata": {}, "outputs": [], "source": [ "asset_CRR = pyop3.binomial_tree(S0, r, T, sigma = sigma, N = 100)\n", "asset_RB = pyop3.binomial_tree(S0, r, T, sigma = sigma, N = 100, tree_type=\"RB\")\n", "\n", "CRR_tree_call_per_strike = np.zeros(401)\n", "RB_tree_call_per_strike = np.zeros(401)\n", "\n", "for i, K in enumerate(np.arange(100,501,1)):\n", " CRR_tree_call_per_strike[i] = pyop3.european_option(asset_CRR, K).fast_put_call()['call']\n", " RB_tree_call_per_strike[i] = pyop3.european_option(asset_RB, K).fast_put_call()['call']\n", " \n", "log_abs_error_CRR = np.log(np.abs(CRR_tree_call_per_strike - analytical_price_per_strike))\n", "log_abs_error_RB = np.log(np.abs(RB_tree_call_per_strike - analytical_price_per_strike))" ] }, { "cell_type": "code", "execution_count": 20, "id": "b9738c85", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(3,2, figsize = (12,12), sharex = True)\n", "fig.suptitle('Comparing Binomial Tree Models vs Analytical Call Price')\n", "\n", "ax[0,0].set_title('Comparing CRR Tree and BS Model')\n", "ax[0,0].plot(strikes, analytical_price_per_strike, label = 'BS')\n", "ax[0,0].plot(strikes, CRR_tree_call_per_strike, label = 'CRR', ls = '-.')\n", "ax[0,0].legend()\n", "ax[0,0].set(ylabel = 'Option Price')\n", "\n", "ax[0,1].set_title('Comparing RB Tree and BS Model for K = 300')\n", "ax[0,1].plot(strikes, analytical_price_per_strike, label = 'BS')\n", "ax[0,1].plot(strikes, RB_tree_call_per_strike, label = 'RB', ls = '-.')\n", "ax[0,1].legend()\n", "ax[0,1].set(ylabel = 'Option Price')\n", "\n", "ax[1,0].set_title('Absolute Pricing Error (CRR Tree vs BS Model)')\n", "ax[1,0].plot(strikes, np.abs(RB_tree_call_per_strike - analytical_price_per_strike)/analytical_price_per_strike * 100**2)\n", "ax[1,0].set(ylabel = 'Absolute Pricing Error (in bps)')\n", "\n", "ax[1,1].set_title('Absolute Pricing Error (RB Tree vs BS Model)')\n", "ax[1,1].plot(strikes, np.abs(RB_tree_call_per_strike - analytical_price_per_strike)/analytical_price_per_strike * 100**2)\n", "ax[1,1].sharey(ax[1,0])\n", "ax[1,1].set(ylabel = 'Absolute Pricing Error (in bps)')\n", "\n", "ax[2,0].set_title('Log Absolute Pricing Error (CRR Tree vs BS Model)')\n", "ax[2,0].plot(strikes, log_abs_error_CRR)\n", "ax[2,0].set(ylabel = 'Log Absolute Pricing Error', xlabel='Strike Level K')\n", "\n", "ax[2,1].set_title('Log Absolute Pricing Error (RB Tree vs BS Model)')\n", "ax[2,1].plot(strikes, log_abs_error_RB)\n", "ax[2,1].sharey(ax[2,0])\n", "ax[2,1].set(ylabel = 'Log Absolute Pricing Error (in bps)', xlabel='Strike Level K')\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1bf9b913", "metadata": {}, "source": [ "Generally, the binomial tree option pricing models do provide a good numerical approximation of the European option prices, however they do come with some limitations. From the above investigation, we see that the binomial tree models achieve good approximations for deep ITM options. However, as the strike level increases towards ATM and OTM levels, the relative pricing error increases significantly, to the point of explosion as we go far out-of-the-money.\n", "\n", "The lower Absolute pricing error (in bps) is achieved for deep ITM call options as deep ITM call options tend to be very expensive. As a result, this brings the relative error low. As we move towards deep OTM call options, the lower option prices resulted in high relative error even when the absolute error remains about the same level. This is evident from the log absolute pricing error charts, where for both tree models the log absolute pricing error did not deviate too much for most of the strike levels, yet the relative error chart exploded as we go dar out-of-the-money.\n", "\n", "From this tutorial, we can conclude that binomial tree models may not more beneficial an alternative to the analytical Black-Scholes model when it comes to computational efficiency and accuracy. Nonetheless, the binomial tree model is fairly useful as a back-of-the-envelope computation of option prices and for learners to quickly grasp the concept of option pricing. The benefits of the binomial tree option pricing model will be accentuated as we delve into more complex options, such as the American-type options which do not have an analytical solution. This will be further discussed in the next tutorials. Thank you!\n", "\n", "© Copyright 2023, Team PyOptionTree." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.7.11" } }, "nbformat": 4, "nbformat_minor": 5 }