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{
"metadata": {
"name": "Monte Carlo Derivative Pricing"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
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"cells": [
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"cell_type": "markdown",
"metadata": {},
"source": "Monte Carlo Methods\n========================\n\nThe value of an option is the risk-neutral expectation of its discounted payoff. **Monte Carlo** methods approximate the expectation operator by an average of a large number of simulated values. For instance, suppose a random variable, $x$ is distributed as $\\mathcal{N}(\\mu, \\sigma^2)$. If we take $M$ draws from this distribution and average them we get an estimate for the expected value:\n$$\\mathbb{E}[x] \\approx \\frac{1}{M}\\sum_{j=1}^{M} x_j $$\n\nThis works well if we are willing to make an assumption about the distribution. You may recall that we use bootstrapping methods when we are not willing to make such an assumption (through resampling). \n\nAs a first step to using **Monte Carlo** methods to price options we want to be able to simulate the path of the underlying security, $\\{S_t\\}_{t=0}^T$. Suppose this process takes the form:\n$$dS_t = (r - \\delta) S_t dt + \\sigma S_t dz_t $$\nWhere $dz_t$ is a Brownian Motion increment. The above process is a **Geometric Brownian Motion**. In this case, the solution to the above stochastic differential euqation is:\n\n$$S_T = S_0 e^{(r - \\delta - \\frac{1}{2}\\sigma^2)T + \\sigma z_T}$$\n\n$$\\mathbb{E}[S_T] = S_0 e^{(r - \\delta - \\frac{1}{2}\\sigma^2)T} $$\n\nHowever, for general cases without a known solution it is useful to be able to simulate the above stochastic process. First, we use **Ito's Lemma** for the process for $x = f(S) = \\ln S$. \n\n$$ dx_t = \\frac{\\partial f(S)}{\\partial s}dS + \\frac{1}{2}\\frac{\\partial^2 f(S)}{\\partial S^2}dS^2 = (r - \\delta - \\frac{1}{2}\\sigma^2)dt + \\sigma dz_t = \\nu dt + \\sigma dz_t$$\n\nThis has been expressed in terms of the infinitesimals, $dz,dt,dx$. We change this to discrete time notation:\n\n$$\\Delta x = \\nu \\Delta t + \\sigma \\Delta z$$\n\nWhich we can express as:\n\n$$x_{t+\\Delta t} = x_t + \\nu \\Delta t + \\sigma (z_{t+\\Delta t} - z_t) $$\n\nWhere $z_{t+\\Delta t} - z_t$ is distributed $\\mathcal{N}(0, \\Delta t)$. Thus, we can draw a sequence of random normals and simulate 100 sequences as follows:"
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"input": "import numpy as np\nfrom matplotlib import pyplot as plt\nimport scipy.stats as ss\n%matplotlib inline\n\ndef sample_path(N = 365, T = 1.0, sig = 0.2, r = .06, delta = .02, S = 100.0):\n dt = 1.0 * T / N\n x = np.zeros(N+1)\n s = np.zeros(N+1)\n eps = sig* np.sqrt(dt) * ss.norm.rvs(size = N, loc = 0, scale = 1)\n \n nu = r - delta - 0.5 * sig ** 2\n x[0] = np.log(S)\n \n for t in range(N):\n x[t+1] = x[t] + nu * dt + eps[t]\n s = np.exp(x)\n return x, s",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 43
},
{
"cell_type": "code",
"collapsed": false,
"input": "sumS = 0.0\nM = 100\nfor j in range(M):\n X,S = sample_path()\n sumS = sumS + S[-1]\n plt.plot(S)\nplt.xlabel('Time')\nplt.ylabel('Stock Price')\nplt.title('Simulated Sample Paths of a Geometric Brownian Motion')\nplt.show()\n\nmeanST = sumS / M\nexpST = 100 * np.exp((.06 - .02 - .5*.2**2)*1)\n\nprint 'The mean of the terminal Values and the Expected Value'\nprint meanST, expST",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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SWLqhQ9n99u5l9xs/HujQAYiJUV52Sbl0CahUCfDxAWbNKjj/7h1w6NDXl/8F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/G/a0H9tj5oWMXnK4f4/EsGRtGvMczIpuTFMTrIG9GJFWTcSSJL0YZrgkRq0gSEV5VQePM2zQN7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"text": "<matplotlib.figure.Figure at 0x127926a0>"
},
{
"output_type": "stream",
"stream": "stdout",
"text": "The mean of the terminal Values and the Expected Value\n105.24957908 102.020134003\n"
}
],
"prompt_number": 44
},
{
"cell_type": "markdown",
"metadata": {},
"source": "We see that the simulations tend to their expected value, which is promising. As well, this gives us a sense of what the stochastic process looks like."
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Valuing European Options is Easy!\n-------------------------------------\n\nMonte Carlo Methods have lots to recommend them for European option pricing problems. We can easily price options with complex underlying stochastic processes by simulating the sample paths and averaging the discounted payoffs. We will go through the example of a European Call Option. For the assignment problem I will have you guys simulate a different stochastic process than the Geometric Brownian Motion.\n\nIn the case of a GBM we know that at time $T$ the stock price is distributed as $\\mathcal{N}(r - \\delta - \\frac{1}{2}\\sigma^2)T, \\sigma^2 T)$. This makes simulation easier and we use this fact in the function below. For general stochastic processes we will use the *SamplePath* function to find the time $T$ stock price. \n\n1. For $m = 1, 2, \\dots, M$ find the time $T$ stock price, $S_T$.\n2. For each $S_T^m$ find the option payoff: $\\max\\{0, S_T - K\\}$.\n3. Average the discounted payoffs: $\\frac{1}{M}\\sum_{m=1}^{M}e^{-rT}C_T^m$\n\nWe may also want to find a measure of how accurate the simulation is. We use the **numerical standard error** for this. We define the numerical standard error as:\n\n$$NSE = \\frac{SD(C_T)}{\\sqrt{M}} $$\n\nSo long as the variance of the call price simulations is finite we can make the error due to sampling variation arbitrarily small by increasing $M$. However, it may take a very large $M$ (i.e. $M > 1,000,000$) to make the NSE very small. This will be apparent in the example below. For this reason **Clemlow and Strickland** discuss various variance reduction techniques. We will not get heavily into these issues, but you should be aware.\n\nWe are now ready to define a function which prices an option via Monte Carlo methods."
},
{
"cell_type": "code",
"collapsed": false,
"input": "def SamplePath(N = 10, T = 1.0, r = .06, div = .03, sig = .2, S = 100.):\n '''\n Simulates the sample path of the process:\n \n dS = nu S dt + sigma S dz\n \n With parameters:\n \n N - numer of time intervals\n T - time until exercise date\n r - risk free interest rate\n div - the dividend payout rate\n sig - the standard deviation or diffusion term\n S - initial security price\n \n Returns:\n S_T - the value of the stock at time T.\n '''\n \n dt = 1.0 * T / N\n nu = r - div - 0.5 * sig ** 2\n x = np.log(S)\n \n for t in range(N):\n eps = sig * np.sqrt(dt) * ss.norm.rvs(size = 1, loc = 0, scale = 1)\n x = x + nu * dt + eps\n s = np.exp(x)\n return s \n\ndef EuroCall(K = 100.0, T = 1.0, S = 100., sig = .2, r = .06, div = .03, N = 10, M = 100, GBM = True):\n '''\n Uses Monte Carlo to price a European Call Option. There are two options for the underlying stochastic process:\n - GBM == True implies that we can draw from a lognormal distribution.\n - GBM == False implies we have to use the SamplePath function to find the time T stock price.\n \n Parameters:\n N - numer of time intervals\n T - time until exercise date\n r - risk free interest rate\n div - the dividend payout rate\n sig - the standard deviation or diffusion term\n S - initial security price\n K - the strike price\n M - number of Monte Carlo simulations\n \n Output:\n 0 - The Call price\n 1 - The Numerical Standard Deviation\n '''\n \n dt = (1.0 * T) / N\n nudt = (r - div - .5 * sig ** 2 ) * dt\n sigdt = sig * np.sqrt(dt)\n lnS = np.log(S)\n \n sumCT = 0.\n sumCT2 = 0.\n nuT = (r - div - 0.5 * sig ** 2) * T\n sigT = sig * np.sqrt(T)\n \n if GBM:\n for j in range(M): \n lnSt = ss.norm.rvs(size = 1, loc = nuT, scale = sigT)\n ST = np.exp(lnSt + np.log(S))\n CT = max(0, ST - K)\n sumCT = sumCT + CT\n sumCT2 = sumCT2 + CT * CT\n \n else:\n for j in range(M):\n ST = SamplePath(N, T, r, div, sig, S)\n CT = max(0, ST - K)\n sumCT = sumCT + CT\n sumCT2 = sumCT2 + CT * CT\n \n callprice = np.exp(-r * T) * sumCT / M\n SD = np.sqrt( (sumCT2 - sumCT2 / M) * np.exp(-2*r*T) / (M-1))\n SE = SD / np.sqrt(M)\n return callprice, SE\n\nCprice, Sterr = EuroCall()\nprint 'The Call Price is : ', Cprice\nprint 'The Numerical Standard Error is: ', Sterr",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "The Call Price is : [ 6.4789156]\nThe Numerical Standard Error is: [ 1.16937516]\n"
}
],
"prompt_number": 70
},
{
"cell_type": "markdown",
"metadata": {},
"source": "You will notice that I took the time to introduce what is called a *docstring* to the two functions above. This is good practice for functions that you will reuse often as you may forget how they work. Notice that when you call the python help function it will return the *docstring*. It is good practice to properly comment your functions."
},
{
"cell_type": "code",
"collapsed": false,
"input": "help(SamplePath)\nhelp(EuroCall)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Help on function SamplePath in module __main__:\n\nSamplePath(N=10, T=1.0, r=0.06, div=0.03, sig=0.2, S=100.0)\n Simulates the sample path of the process:\n \n dS = nu S dt + sigma S dz\n \n With parameters:\n \n N - numer of time intervals\n T - time until exercise date\n r - risk free interest rate\n div - the dividend payout rate\n sig - the standard deviation or diffusion term\n S - initial security price\n \n Returns:\n S_T - the value of the stock at time T.\n\nHelp on function EuroCall in module __main__:\n\nEuroCall(K=100.0, T=1.0, S=100.0, sig=0.2, r=0.06, div=0.03, N=10, M=100, GBM=True)\n Uses Monte Carlo to price a European Call Option. There are two options for the underlying stochastic process:\n - GBM == True implies that we can draw from a lognormal distribution.\n - GBM == False implies we have to use the SamplePath function to find the time T stock price.\n \n Parameters:\n N - numer of time intervals\n T - time until exercise date\n r - risk free interest rate\n div - the dividend payout rate\n sig - the standard deviation or diffusion term\n S - initial security price\n K - the strike price\n M - number of Monte Carlo simulations\n \n Output:\n 0 - The Call price\n 1 - The Numerical Standard Deviation\n\n"
}
],
"prompt_number": 71
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Valuing American Options is not as Easy!\n-----------------------------------------------\n\nValuing American style options via Monte Carlo methods is more challenging due to early exercise. If there are no dividends then we can use the fact that it is not optimal to exercise a call early to simplify the problem (for call options only!). However, the beauty of the Monte Carlo approach is that we can flexibly account for dividends in the stochastic process for the stock price. This introduces the possibility of early exercise, which is problematic. The chapter on Monte Carlo Methods in Clemlow and Strickland is silent on how to handle American Options. I found a couple papers by students that summarize approaches to the problem that may be useful as starting points for those interested.\n\n- http://www.math.wustl.edu/~feres/Math350Fall2012/Projects/mathproj07.pdf\n- http://www2.math.uu.se/research/pub/Jia1.pdf\n\nYou may find this type of report at a more accessible level. If you really wanted to get into this material then the references cited within could be useful."
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Assignment Problem:\n---------------------\n\nThe assignment problem is to:\n\n1. Write a function which simulates the sample path for the following stochastic process:\n \n $$dS = \\theta(r - \\delta - S)dt + \\sigma dz $$\n\n Where $dz$ is a **Brownian Motion** increment. \n\n2. Plot 100 sample paths of the process and compare the results to the **Geometric Brownian Motion** presented in the lecture notes. What is a key difference between the two processes? *Hint: This is an Ornstein-Uhlenbeck Process and it has a nice Wikipedia article! Think about what happens to the variance as $T\\to \\infty$.*\n\n3. Write a function that uses the sample path function to generate 200 realizations of the process and return the Monte Carlo estimate of the Call Price as well as the numerical standard deviation of the estimate.\n\n **The following are bonus questions.**\n\n4. Now write a new sample path function that simulates the following **Cox-Ingersoll-Ross** process, which is used to model interest rates:\n \n $$dS = \\theta(r - \\delta - S)dt + \\sigma\\sqrt{S} dz $$\n \n Simulate its sample paths and compare it to the previous two stochastic processes. It should be easy to amend your call pricing function to price a security with this underlying process. Do so. \n \n5. Write a loop that uses the call pricing function and any of the above stochastic processes to calculate the price and numerical standard deviation of a European Call for $M = \\{200, 300, 500\\}$. Plot the estimated price and standard deviation. What do you notice? "
}
],
"metadata": {}
}
]
}
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