FIN5615_Project_2_Mark_Shust_tun83295.ipynb

{
 "cells": [
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   "cell_type": "markdown",
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   "source": [
    "<h2>FIN5615 Project #2\n",
    "    <p class=\"text-primary\">Random Walk Simulaton</p>\n",
    "</h2>\n",
    "\n",
    "<div class = \"alert alert-block alert-danger\">\n",
    "    <b>Due Date</b>: October 12th 2020, 11:59PM EST\n",
    "</div> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-success\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:black\"><b>Project Introduction</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    In this project we will try to address some of the shortcomings of modeling stock price as a simple random walk. We will compare the simulated option prices from our random walk model against that of the Black-Scholes options pricing formula.\n",
    "    </div>\n",
    "</div>\n",
    "<div class = \"panel panel-info\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:black\"><b>Instructions</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    Please code you solutions directly in this Notebook under each task in the cells provided below. Include all code used to produce your results, and support your answers with textual explanations if neccessary. You may feel free to add additional Code and/or Markdown cells as needed. Code must be written using <b>Python 3</b>.\n",
    "    <br><br>Please order the cells in your Notebook in the order in which they are intended to run! It is expected that your Notebook is able to run in sequence from start to finish without any errors (before submitting check by: <code>Kernel > Restart & Run All</code>).\n",
    "    <br><br>Once ready, please submit your assignment as an <b>.ipynb file</b> (<code>File > Download as > Notebook</code>). You must name your files in the following format: <b><code>FIN5615_Assignmnet_1_Richard_Lee_tuc12345.ipynb</code></b>.\n",
    "    </div>\n",
    "</div>\n",
    "\n",
    "---\n",
    "<div class = \"alert alert-block alert-warning\">\n",
    "    <b>Note</b>: Import all libraries that you plan on using in the code block below.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 1</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    Continue with the example of Ford (F) stock price from the end of Lecture 3. Assume that daily price movements of F follow a simple random walk, and that the price of F today is \\$5.\n",
    "    <ul>\n",
    "        <li>Simulate the price of F over the next year (250 trading days) for 1000 trials.</li>\n",
    "        <li>Plot the histogram of the probability distribution of F's stock price at the end of the year.</li>\n",
    "    </ul>\n",
    "    <br>Set the random seed to 5615 at the beginning of your code.\n",
    "    <p style=\"text-align:right;\">[5pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(5615)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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lwCeA55I807XdCWwCtia5md4ZYjdMqL4T7dPAQ0n+Cvg+vW98zfMKVUlq0JJclpGk1hnuktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGGuyQ16P8B57CckX3RyGwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#establishing variables\n",
    "starting_price = 5\n",
    "steps = 250\n",
    "trials = 1000\n",
    "\n",
    "#simulation\n",
    "sims = []\n",
    "for trial in range(trials):\n",
    "    random_path = [starting_price]\n",
    "    for step in range(steps):\n",
    "        if random.random() < .5:\n",
    "            price_change = 1\n",
    "        else:\n",
    "            price_change = -1\n",
    "\n",
    "        random_path.append(random_path[-1] + price_change)\n",
    "    sims.append(random_path)\n",
    "    \n",
    "\n",
    "ending_prices = [trial[-1] for trial in sims]\n",
    "#histogram plotting\n",
    "plt.hist(ending_prices)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 2</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    One problem that arises when naively modeling stock price as a random walk is that simulated prices are not guarenteed to be positive. In the case of a simple random walk, we are assuming stock prices change by an arbitrary +\\$1 or -\\$1 at each time step.\n",
    "    <br><br>Instead of assuming a price movement of +\\$1 or -\\$1, modify the random walk's possible price movement to be either +1% or -1% (equivalently, a mutiplicative factor of 1.01 or 0.99):\n",
    "    <br><br>\n",
    "    $$X_{t+1} = \\left\\{\n",
    "        \\begin{array}{ll}\n",
    "            X_t \\times 1.01 & \\quad p = 0.5 \\\\\n",
    "            X_t \\times 0.99 & \\quad p = 0.5\n",
    "        \\end{array}\n",
    "    \\right.$$\n",
    "    <ul>\n",
    "        <li>Simulate the price of F under this new dynamic over the next year (250 trading days) for 1000 trials.</li>\n",
    "        <li>Plot a histogram of the probability distribution of F's stock price at the end of the year.</li>\n",
    "        <li>Explain why making this adjustment prevents the stock price from becoming negative.</li>\n",
    "    </ul>\n",
    "    <br>Set the random seed to 5615 at the beginning of your code.\n",
    "    <p style=\"text-align:right;\">[10pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "random.seed(5615)\n",
    "\n",
    "starting_price = 5\n",
    "steps = 250\n",
    "trials = 1000\n",
    "\n",
    "sims = []\n",
    "for trial in range(trials):\n",
    "    random_path = [starting_price]\n",
    "    for step in range(steps):\n",
    "        if random.random() < .5:\n",
    "            price_change = 1.01\n",
    "        else:\n",
    "            price_change = .99\n",
    "\n",
    "        random_path.append(random_path[-1] * price_change)\n",
    "    sims.append(random_path)\n",
    "len(sims)\n",
    "\n",
    "ending_prices = [trial[-1] for trial in sims]\n",
    "len(ending_prices)\n",
    "\n",
    "#plotting\n",
    "plt.hist(ending_prices , density = True, bins= 15,color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Becasue we use .99 as the down factor we can never hit 0 it will get infinetly small but never zero becasue we just take a smaller and smaller peice of the starting value.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 3</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    Another issue with our current random walk model is that the magnitude of the stock price's movement is the same regardless of the frequency of our simulation.\n",
    "    <br><br>For example, if we simulate quarterly increments, then the stock price can exhibit only 4 up or down movements of 1% within one year, whereas if we simulate in daily increments the stock price can have 250 up or down movements of 1% within one year, resulting in a much wider distribution of ending prices. This type of behavior is unreasonable.\n",
    "    <br><br>We can try to remedy this by adjusting the magnitude of the stock price movement by the \"step size\" (h) of our simulation:\n",
    "    <br><br>\n",
    "    $$X_{t+1} = \\left\\{\n",
    "        \\begin{array}{ll}\n",
    "            X_t \\times (1 + 0.01\\sqrt{h}) & \\quad p = 0.5 \\\\\n",
    "            X_t \\times (1 - 0.01\\sqrt{h}) & \\quad p = 0.5\n",
    "        \\end{array}\n",
    "    \\right.$$\n",
    "    <br>Under this new model specification, we can interpret 1% as the percentage movement in stock price over an annual period, and multiplying it by $\\sqrt{h}$ scales it for the length of time for a single period of our simulated random walk, where $h = \\frac{1}{steps}$. For example, under daily increments, $h = \\frac{1}{250}$.\n",
    "    <ul>\n",
    "        <li>Simulate the price of F under this new dynamic over the next year (250 trading days) for 1000 trials.</li>\n",
    "        <li>Plot a histogram of the probability distribution of F's stock price at the end of the year.</li>\n",
    "    </ul>\n",
    "    Set the random seed to 5615 at the beginning of your code.\n",
    "    <p style=\"text-align:right;\">[10pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(5615)\n",
    "\n",
    "starting_value = 5\n",
    "steps = 250\n",
    "trials = 1000\n",
    "\n",
    "sims = []\n",
    "for trial in range(trials):\n",
    "    random_path = [starting_value]\n",
    "    for step in range(steps):\n",
    "        if random.random() < .5:\n",
    "            price_change = (1 + (.01 * np.sqrt(1 / steps)))\n",
    "        else:\n",
    "            price_change = (1 - (.01 * np.sqrt(1 / steps)))\n",
    "\n",
    "        random_path.append(random_path[-1] * price_change)\n",
    "    sims.append(random_path)\n",
    "len(sims)\n",
    "\n",
    "ending_prices = [trial[-1] for trial in sims]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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u9IZr9gFcyuADeZ8D3tBNv4Tehg4wA5zWtb+Q3p7kmVPah/XAM7rpG4D3dNNnAt+hdxBvXTe91vqwDnh23zIPsQoHwIDnAmf0Tf8ncNm8ZV7NiQcjvzpN22HMPkzFdhi1H33LXs+JB1RPp3dA+3yeOqD60jXWh5HXHfWx5oZlFpLkPcBcVe0G3g58KMkf0/v37A1VVUl+A3hPkqPAMeDNVfXY6lV9onl9uBT4iyRFb0jjWoCqeizJn9O7fw/0AnNN9YHeF+7fJ3mS3n+P762qb65CuWcDtySBXkDsqqrPJ3kzQFV9kN4xm63APuCnwBu7edOyHZbcB6ZnO8AI/Ujy88AcvZMlnkzyNnpfRo9nOm53suQ+0PtyPWndcYrxClVJatBaHHOXJA1huEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1KD/B7OyshBswBPPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ending_prices, color = \"orange\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 4</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    Another issue with our current random walk model is that our assumed annual magnitude of the stock price's movement is the same 1% regardless of the risk profile of the company. For example, an annual movement of 1% might seem reasonable for F, but definitely not for TSLA stock.\n",
    "    <br><br>We can try to account for this by including the stock's annual volaility as another input parameter to our random walk simulation. Recall that the volatility is a measure of the disperson (a.k.a. standard deviation) on a stock's *continuously compounded returns*.\n",
    "    <br><br>So, we can replace our arbitrary value of 1% with a change in the stock's return in that time step in terms of its annual volatility ($\\sigma$), applied as continuously compounded factors, $u$ and $d$:\n",
    "    <br><br>\n",
    "    $$X_{t+1} = \\left\\{\n",
    "        \\begin{array}{ll}\n",
    "            X_t \\times u = X_te^{\\sigma\\sqrt{h}} & \\quad p = 0.5 \\\\\n",
    "            X_t \\times d = X_te^{-\\sigma\\sqrt{h}} & \\quad p = 0.5\n",
    "        \\end{array}\n",
    "    \\right.$$\n",
    "    <br>Assume that the annual volatility of F's returns is 10%:\n",
    "    <ul>\n",
    "        <li>Simulate the price of F under this new dynamic over the next year (250 trading days) for 1000 trials.</li>\n",
    "        <li>Calculate F's simulated annual rate of return for each of the 1000 trials. Plot this distribution of annual returns in a histogram.</li>\n",
    "        <li>Calculate F's average simulated annual rate of return.</li> \n",
    "    </ul>\n",
    "    Set the random seed to 5615 at the beginning of your code.\n",
    "    <p style=\"text-align:right;\">[10pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(5615)\n",
    "\n",
    "starting_value = 5\n",
    "step = 250\n",
    "steps = 1/step\n",
    "trials = 1000\n",
    "volatility = .1\n",
    "\n",
    "sims = []\n",
    "for trial in range(trials):\n",
    "    random_path = [starting_value]\n",
    "    for change in range(step):\n",
    "        if random.random() < .5:\n",
    "            price_change = (np.exp(volatility * np.sqrt(steps)))\n",
    "        else:\n",
    "            price_change = (np.exp(-volatility * np.sqrt(steps)))\n",
    "\n",
    "        random_path.append(random_path[-1] * price_change)\n",
    "    sims.append(random_path)\n",
    "\n",
    "end_price = [trial[-1] for trial in sims]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.32 %\n"
     ]
    }
   ],
   "source": [
    "annual_rate = []\n",
    "for k in end_price:\n",
    "    total = np.log(k/starting_value)\n",
    "    annual_rate.append(total)\n",
    "\n",
    "plt.hist(annual_rate, color = \"orange\", bins = 15)\n",
    "plt.show()\n",
    "\n",
    "print(round(np.mean(annual_rate),4)*100,\"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 5</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    It is not very realistic to model 0% rates of return on stock prices. It is generally the investor's belief that stock prices will increase over time, although at what rate is unclear. For now, let's assume that the expected return on the stock is equal to the risk-free rate.\n",
    "    <br><br>We can achieve this by adjusting the probabilities associated with an up or down movement in the stock price from 50% to a varying value of $p$, such that on average we receive the risk free rate of return (I will skip over the math here, but this is the idea of risk-neutral pricing):\n",
    "    <br><br>\n",
    "    $$X_{t+1} = \\left\\{\n",
    "        \\begin{array}{ll}\n",
    "            X_t \\times u = X_te^{\\sigma\\sqrt{h}} & \\quad p = \\frac{e^{rh} - d}{u - d} \\\\\n",
    "            X_t \\times d = X_te^{-\\sigma\\sqrt{h}} & \\quad 1 - p\n",
    "        \\end{array}\n",
    "    \\right.$$ \n",
    "    <br>Notice that the value of $p$ will now vary at each step of the random walk, and depends on the values of $u$ and $d$, which are just the multiplicative factors on the stock price that we defined previously.\n",
    "    <br><br>Assume that the annual volatility of F's returns is 10% and a risk-free rate of 1%:\n",
    "    <ul>\n",
    "        <li>Simulate the price of F under this new dynamic over the next year (250 trading days) for 1000 trials.</li>\n",
    "        <li>Plot a sample of 100 paths from the simulation on a single line plot.</li>\n",
    "        <li>Calculate the average path for F's stock price over the 1000 trials. Plot this as a line plot.</li>\n",
    "        <li>Calculate F's average simulated annual rate of return. Is it close to our assumed risk-free rate?</li>\n",
    "    </ul>\n",
    "    <br>Set the random seed to 5615 at the beginning of your code.\n",
    "    <p style=\"text-align:right;\">[15pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#random.seed(5615)\n",
    "\n",
    "starting_price = 5\n",
    "steps = 250\n",
    "trials = 1000\n",
    "volatility = .1\n",
    "risk_free = .01\n",
    "u = np.exp(volatility*np.sqrt(1/steps))\n",
    "d = np.exp(-volatility*np.sqrt(1/steps))\n",
    "p = (np.exp(risk_free*(1/steps))-d)/(u-d)\n",
    "\n",
    "sims = []\n",
    "for trial in range(trials):\n",
    "    random_path = [starting_price]\n",
    "    for step in range(steps):\n",
    "        if random.random() < p:\n",
    "            price_change = (np.exp(volatility * np.sqrt(1/steps)))\n",
    "        else:\n",
    "            price_change = (np.exp(-volatility * np.sqrt(1/steps)))\n",
    "\n",
    "        random_path.append(random_path[-1] * price_change)\n",
    "    sims.append(random_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(100):\n",
    "    plt.plot(sims[i])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "steps = 250\n",
    "average_path = []\n",
    "for step in range(steps):\n",
    "    average_price = np.mean([trial[step] for trial in sims])\n",
    "    average_path.append(average_price)\n",
    "plt.plot(average_path,color = \"orange\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.3238 %\n"
     ]
    }
   ],
   "source": [
    "annual_rate = []\n",
    "for k in end_price:\n",
    "    total = np.log(k/starting_value)\n",
    "    annual_rate.append(total)\n",
    "np.mean(annual_rate)\n",
    "print(round(np.mean(annual_rate)*100,4),\"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 6</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    The model we have now is the <b>Cox-Ross-Rubinstein Binomial Tree</b>, and is a much better approximation of stock price movements compared to a simple random walk. We can even price options contracts using this model.\n",
    "    <br><br>Continue to assume that F is worth \\$5 today, with an annual volatility of 10%, and risk-free rate at 1%. \n",
    "    <ul>\n",
    "        <li>Using the simulation results from the previous task, for each of the 1000 trials, calculate the terminal payoff of a call option with strike of $5.50 that expires 1 year from today.</li>\n",
    "        <li>What is the simulated average payoff of this call option?</li>\n",
    "        <li>What is the present value of the simulated average payoff of this call option? This is the Binomial Tree's simulated option price.</li>\n",
    "        <li>Compare this value against the price under the Black-Scholes options pricing formula (you do not have to do this in python). How close are the two prices?</li>\n",
    "    </ul>\n",
    "    <p style=\"text-align:right;\">[10pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(5615)\n",
    "\n",
    "starting_price = 5\n",
    "steps = 250\n",
    "trials = 1000\n",
    "volatility = .1\n",
    "risk_free = .01\n",
    "strike = 5.5\n",
    "u = np.exp(volatility*np.sqrt(1/steps))\n",
    "d = np.exp(-volatility*np.sqrt(1/steps))\n",
    "p = (np.exp(risk_free*(1/steps))-d)/(u-d)\n",
    "\n",
    "sims = []\n",
    "for trial in range(trials):\n",
    "    random_path = [starting_price]\n",
    "    for step in range(steps):\n",
    "        if random.random() < p:\n",
    "            price_change = (np.exp(volatility * np.sqrt(1/steps)))\n",
    "        else:\n",
    "            price_change = (np.exp(-volatility * np.sqrt(1/steps)))\n",
    "\n",
    "        random_path.append(max(random_path[-1] * price_change - strike,0.))\n",
    "    sims.append(random_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average call payoff with strike 5.5 is $ 0.0199\n"
     ]
    }
   ],
   "source": [
    "average_payoff = round(np.mean(sims),4)\n",
    "print(\"The average call payoff with strike\",strike,'is $',average_payoff,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0197\n"
     ]
    }
   ],
   "source": [
    "PV = average_payoff * np.exp(-risk_free)\n",
    "print(round(PV,4))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In python we get .0197 with Derivagem we get .057 which would be 6 cents. Im not sure why we are of i think it might be the time difrence or the simulation is closer to the real value.Derivagem uses calnder days not trading days so that may play a part."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "*Your written response here*\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 7</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    We can further improve our simulated option price to match the Black-Scholes options price, by (1) using more steps in our binomial tree, i.e. smaller step sizes, and (2) increasing the number of trials.\n",
    "    <br><br>Reprice the call option on F using 1000 steps and 5000 trials (this will take more computation time). How does the simulated price compare to the Black-Scholes options price?\n",
    "    <br><br>Set the random seed to 5615 at the beginning of your code.\n",
    "    <p style=\"text-align:right;\">[15pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The new large trial average call payoff with strike $ 5.5 is $ 0.005\n",
      "0.005\n"
     ]
    }
   ],
   "source": [
    "random.seed(5615)\n",
    "\n",
    "starting_price = 5\n",
    "steps = 1000\n",
    "trials = 5000\n",
    "volatility = .1\n",
    "risk_free = .01\n",
    "strike = 5.5\n",
    "u = np.exp(volatility*np.sqrt(1/steps))\n",
    "d = np.exp(-volatility*np.sqrt(1/steps))\n",
    "p = (np.exp(risk_free*(1/steps))-d)/(u-d)\n",
    "\n",
    "sims = []\n",
    "for trial in range(trials):\n",
    "    random_path = [starting_price]\n",
    "    for step in range(steps):\n",
    "        if random.random() < p:\n",
    "            price_change = (np.exp(volatility * np.sqrt(1/steps)))\n",
    "        else:\n",
    "            price_change = (np.exp(-volatility * np.sqrt(1/steps)))\n",
    "\n",
    "        random_path.append(max(random_path[-1] * price_change - strike,0.))\n",
    "    sims.append(random_path)\n",
    "\n",
    "    \n",
    "average_payoff = round(np.mean(sims),4)\n",
    "print(\"The new large trial average call payoff with strike $\",strike,'is $',average_payoff,)\n",
    "\n",
    "PV = average_payoff * np.exp(-risk_free)\n",
    "print(round(PV,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 8</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    Tesla (TSLA) stock price is currently \\$1400, with an annual volatility of 70%. Assume a risk-free rate of 1%. Assume a 6-month put option with a strike of \\$1200.\n",
    "    <ul>\n",
    "        <li>Determine the price of this put option by simulating a CRR binomial tree with 5000 trials and using 1000 steps. Compare the simulated option price against the Black-Scholes options price.</li>\n",
    "        <li>Plot the average simulated TSLA stock price over the 5000 trials. How does TSLA's simulated average path compare against F?</li>\n",
    "        <li>If simulations from the CRR Binomial Tree can give option prices similar to the Black-Scholes model, then why do we still use the latter? Under what situations might we prefer simulations over the Black-Scholes model?</li>\n",
    "    </ul>\n",
    "    Set the random seed to 5615 at the beginning of your code.\n",
    "    <p style=\"text-align:right;\">[25pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Tesla average put payoff with strike $ 1200 is $ 1424.7149\n",
      "The PV of a Tesla put is  1417.6091\n"
     ]
    }
   ],
   "source": [
    "random.seed(5615)\n",
    "\n",
    "t = .5\n",
    "steps = 100\n",
    "trials = 500\n",
    "starting_price = 1400\n",
    "volatility = .7\n",
    "risk_free = .01\n",
    "strike = 1200\n",
    "\n",
    "u = np.exp(volatility*np.sqrt(1/steps))\n",
    "d = np.exp(-volatility*np.sqrt(1/steps))\n",
    "p = (np.exp(risk_free*(1/steps*t))-d)/(u-d)\n",
    "\n",
    "sims = []\n",
    "for trial in range(trials):\n",
    "    random_path = [starting_price]\n",
    "    for step in range(steps):\n",
    "        if random.random() < p:\n",
    "            price_change = (np.exp(volatility * np.sqrt(1/steps)))\n",
    "        else:\n",
    "            price_change = (np.exp(-volatility * np.sqrt(1/steps)))\n",
    "\n",
    "        random_path.append((random_path[-1] * price_change))\n",
    "    sims.append(random_path)\n",
    "\n",
    "    \n",
    "average_payoff = round(np.mean(sims),4)\n",
    "print(\"The Tesla average put payoff with strike $\",strike,'is $',average_payoff,)\n",
    "\n",
    "PV = average_payoff * np.exp(-risk_free*t)\n",
    "print(\"The PV of a Tesla put is \",round(PV,4))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "steps = 100\n",
    "average_path = []\n",
    "for step in range(steps):\n",
    "    average_price = np.mean([trial[step] for trial in sims])\n",
    "    average_path.append(average_price)\n",
    "plt.plot(average_path,color = \"orange\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your written response here*\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def generate_weiner_diffs(n, delta):\n",
    "    return [np.random.normal(loc=0.0, scale=np.sqrt(delta)) for _ in range(n)]\n",
    "\n",
    "def single_iter(rt, a, b, delta, sigma, weiner_diff):\n",
    "    return rt + a*(b-rt)*delta + sigma*np.sqrt(rt)*weiner_diff\n",
    "\n",
    "def run_sim(n, a, b, r0, sigma, delta):\n",
    "    output = [ r0 ]\n",
    "    weiner_diffs = generate_weiner_diffs(n, delta)\n",
    "    for i in range(n):\n",
    "        output.append(single_iter(output[i], a, b, delta, sigma, weiner_diffs[i]))\n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "a= 0.150171427\n",
    "b= 0.013625329\n",
    "sigma = 0.00288994\n",
    "r0 = .0266\n",
    "delta = 0.01\n",
    "N = 800\n",
    "\n",
    "test_run_1 = run_sim(N, a, b, r0, sigma, delta)\n",
    "test_run_2 = run_sim(N, a, b, r0, sigma, delta)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x116aeea10>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "total_time = delta*N\n",
    "time_axis = np.linspace(0, total_time, N+1) # N+1 to account for r0\n",
    "plt.plot(time_axis.tolist(), test_run_1)\n",
    "plt.plot(time_axis.tolist(), test_run_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}