{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Particle Filters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Particle filters are a version of thompson sampling that allow us to approximate the probability distribution of different parameters. This is often seen in the world of pricing inventory. It is most useful for pricing individual items that sell one at a time; however, it is highly flexible and can be used to model many different problems.\n", "\n", "We will be focusing on stocks and mean reversion, meaning we are going to model the \"true\" value of a stock using a particle filter and Thompson Sampling. We will also see how this can be used to inform a trading strategy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*******\n", "\n", "Imagine being god of the stock market for a moment. Being gods, we know the stock of company LRW is actually worth \\\\$45, its average or so called \"true\" value. Currently, the stock is priced at \\\\$40. The market value of this stock tends to fluctuate around the actual value, as stocks do. Sometimes the price creeps up and sometimes it creeps down, but eventually it will revert to this average (which we call 'mean reversion').\n", "\n", "The investors of the stock market are not privy to this information. Therefore, to them the true of LRW stock is a random variable (this is a Bayesian concept and one that is very useful for time series problems). For now, we will assume that the \"true\" value of LRW does not change over time.\n", "\n", "Starting with this initial value, the investors can begin to form a prior for the mean or true value of this stock. However, they do not want to assume too much since we have no information about whether this is above or below the mean. Say they choose a relatively naive prior. Perhaps we will start with a normally distributed variable with a standard deviation of 5: $$ V_{LRW} \\sim \\text{Normal}(40, 5) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this example, the particle filter will take on the role of the prior and posterior distributions for mu. Then using Thompson Sampling, we can estimate the probability that the market value of LRW is above or below the true value of the mean and use this to inform our decision to trade or not. This problem is slightly different from the Multi-Armed Bandit in that we are not required to take an action in order to learn more about the environment. However, it *can* be used for explore-exploit strategies when trading low-volume inventory or when you have enough influence in the market to affect prices. For now, we will assume the point of view of the ordinary investor." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A particle filter is a discrete representation of our prior and posterior, so to do this we take our continuous prior and select some range of possible values for $V$. Although LRW is not particularly volatile, let's set this range to \\\\$20 all the way to \\\\$60." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.stats import norm\n", "\n", "V = np.arange(20, 60.1, .25)\n", "P_V = norm.pdf(V, loc=40., scale=5)\n", "P_V = P_V / P_V.sum() # So that altogether it equals 1" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.plot(V, P_V)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For convenience, let's say that the true variance of the stock price $SP_{LRW} = 5$ so that at any given time the actual curve looks like this:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(V, P_V)\n", "P_SP = norm.pdf(V, loc=45, scale=5)\n", "P_SP = P_SP / P_SP.sum()\n", "plt.plot(V, P_SP)\n", "plt.vlines(45, 0, .021, color='red')\n", "plt.legend(['Prior of V', 'Distribution of SP', 'Actual Value of V'])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the value we are trying to estimate is not the same as the prices we observe. What we see is simply the market price $SP_{LRW}$. The actual value of $V_{LRW}$ is unknown. So while our prior and posterior is based on the distribution of $V_{LRW}$, it will be modified by a Gaussian/Normal distribution based on the variable $SP_{LRW}$. Perhaps this will also explain why, in the previous Mulit-Armed Bandit problem, we had two different distributions: A binomial/Bernoulli distribution for the likelihood function and a Beta distribution for the prior/posterior. The parameter $p$ from the binomial distribution is the parameter we were trying to estimate and the $\\alpha$ and $\\beta$ from the Beta distribution were *hyper*parameters meant to help estimate $p$.\n", "\n", "In this example, we do not tune any parameters in truth. Because it is discrete, the particle filter can take the shape of any probability distribution, so no hyperparameters. We could use it to estimate both mean and variance of the orange curve, but to keep things 1-dimensional, we will simply try to find the red line, or the mean of the orange curve.\n", "\n", "*******" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So let's get started!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Going back to Bayes' Rule:\n", "\n", "$$ \\text{Posterior } \\propto \\text{ Likelihood } \\cdot \\text{ Prior} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The prior and posterior are both represented by the particle filter, so the only thing we need to worry about is the likelihood function $P(sp|V_{LRW})$, or the probability of observing a stock price given a true value for LRW. It's kind of like drawing a probability distribution in reverse." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sp = 38.\n", "\n", "# The probability of seeing a value of 38 given different values of V\n", "for V_test in range(20, 61, 5):\n", " y = norm.pdf(V, loc=V_test, scale=5)\n", " plt.plot(V, y, color='blue')\n", "plt.vlines(sp,0,.081,color='red')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "L = lambda sp: norm.pdf(sp, loc=V, scale=5)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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nIuF+FLhO0n5JY8DtwOGVLcvM2nqdOAw8NGO95YZ7RDSAu4BHgaeAhyPiSUn3SboVQNKPSToJ/BzwW5KeXMmizdaTbuHe7rl7aMZ6KTTmHhFHgCMd992buX2UZLjGzJZZ12X22sMy7rlbD/6GqlnJ9R2Wcc/denC4m5Vcs8cyewDOduvF4W5Wct167mMjyVt33uf9tR4c7mYl120lpq3jyeGy6dfmh1GSVYDD3azkuvXct28cBeCMw916cLiblVyjy2IdDnfL43A3K7luy+w53C2Pw92s5Lots7ctDffp2cYwSrIKcLiblVy3U/5uG0/D3T1368HhblZy3U4cNj5aZ8NIzcMy1pPD3azkml2W2YNk3P3MjMPdunO4m5Vct547JOE+Petwt+4c7mYlFhFdx9whOajqYRnrxeFuVmLtc8f06rk73K0Xh7tZiTXSVbA757mDw936c7iblVia7b3H3B3u1oPD3azE+vXct42PcHau4XVUrSuHu1mJtRfj6BruG0eJgLP+lqp14XA3K7FGGu69hmXA55ex7hzuZiW22HPv/iUmwHPdrSuHu1mJNd1zt0vkcDcrsQuNPgdUHe7Wh8PdrMSeOX0OgGsv33TRY+65Wz8jwy7AbF1rzsPcWZg9k1w3ZpP7WvPQbDDzre/zk7W/4O2vzMAVLwOCJ/8L1OrsaIqfqH2DLafOwMm3wNjm9LIluR7ZMOzfzoZIEcOZIzsxMRGTk5NDeW2zFdFqwrkX4fyLcG4Kzne5zLwEs9NJkM9NJ2G+UmqjSchvvAw2XQ6bdsLmnbBpR3J70+WweRdsfSNsuyq5r8uBWysXSY9HxEReO/fczYqIgJmX4cwJmD4FZ07B9Mn0Ot0++wNodZlzXt8AW65Ig/Vy2PEm2LA1vWxPrse3JT3u0U1QH0mCuT7KwS98g2uv2M6v/fT18KE7QcDnHkxeJ5r8vQf+N+/Zv41ffOeVcOEcXDifXs4m13PnYPZVOH8azj4HL3w7ud2cu7jO2mgS9Ft3w7bdsPWq9Hp3Ev7b9iTX/h9BJTjczSDpTbdDuleAd/aya6OwfQ9s2wvXvjsJv+17YMsbkx7x5p1JqI9tAV18QDTP2dl5/uTVKf7pTW+BK66D18aTB648sNDmxKYzfKO+Dd7yjuJPHAHzM0nIt0P/7HPJ7zj9XPIh9cIxOP7l5AOj0+YrkpDfvncx8Nu3t+9JPgzqowP/vra8HO629s2/1qWnfTIT4KeSIZIs1ZKQ3r4Hdl8Pb71laYBt25sE+AoOY3zn+bMAHLhqW882l3TaX2lxfP4N1/ZvOzu9GPxnTsH0Dxb340vfhe/9z4v3HYItV6b76apkX23fk34QZD4A646flVRo70q6GfgMUAceiIjf6Hh8A/AfgR8FXgJ+PiKeXd5SzTo05uDcC8k497kXlt4++/xigM+8dPHPbtqZhMyON8H+96Shs3cxwLe+cei9z2M/SELzwO7tPdus+Jkhx7cll11v7d1mdnpp6E9nhqqmnobjj8H8+aU/k/3wbO/79tBP+/amnTAytnK/2xqXG+6S6sD9wAeBk8BRSYcj4lim2YeBVyLihyTdDvwm8PMrUbCtQRFJ73puGl57JRnbfu0VeO3li7dnXkkOTJ57IRlL7mbT5YvBsedHF3va2d7j6Piq/oqX4tgPptmxeYwrt/Ue496+cZQTL8+sYlVdtD8Arnhb98cjktlA02nPv/2h2779wrfh/z0Kjdcu/tkN25MDwJt3pgeEsweGd8LGNySvvWEbjG9Pj11s9YFhivXcbwKOR8QzAJIeAm4DsuF+G/CJ9PYjwL+XpBjWVBwrLiI5ONdqLhykS25ntxtL72vOJb3mxmyf68zt+dnFg3xz55Jx3Ln27fQ6mr1rrI0mb/CNO5I38xVvgze9LxnP3nJleklvb9419B73cjn23DQ/fNU21Ge8ftv4CK/MXOC1C002jtVXsboBSMmMnY2XwZU/3L1NRPIBnj04ff508r+u86dh5nTyQfDcE8l2q9//VpSG/bbF69FNMLqxz3Xm9siGhQPa1EeL31YNavXk+hKOsSy3IuG+BziR2T4JvLNXm4hoSDoDXA6cXo4is47+wWe44tu/nW4tfnYoe7vjM2Xpbu7xMwXadLYTsfColvF56fG7dL724PW2qKeXGi3qNKmxcp+/LcQcY8wzygzjzGgjMySX87qMGXZzXhuZqW3kPBs5r01Ms5VpbeEMWzmjrZyJLbzGOFwQXADOXPw6yb/CS+mluyLdjCJ7olh3Jb9Rked5eeYCv/ieN/Vts3v7OK/OzHP9rz/K1Ts2UStBqLx+G4E3p5cOAjYHm5lhe5xha5xnc5xjc8ywOc6zJc6nt2fYMnOOzedn2Bzn2BAvMc4cG2KODcwxHnOMM0ud1or8Bi2UvsuS66C2uK0az9x4Dzfe+pEVee22VT2iIekgcBDgmmuuuaTnGN26i5c2Lf7BRya+src7Pzl7RV50xF9ne0kdbZbq+fM93mS92qcvNli9uvh+XfSziz8f6R9WS3WCOk3VCWrJtdK4T+9raSRpS51QnSZJm6bqNDSWXGrJZT7dnq+N0dCGhdst6n17nV1+DQDG08uVS36DwZ/nUttc9O9yKa9T5FVyGtUl/vZNmffJV796UZtfet+bOXDVNr72vZc5+XKXYY01axvwRgDOp5dLUYsGY61ZxmKO0ZhjQ2uWkZinHg3qMU+dJvVopPc1qbF4u7ONCGrRTK5pocjEe7SWPL59x/7X88vvlJT9ktChiDjU2Sj3S0yS3g18IiJ+Mt2+ByAi/nWmzaNpm/8jaQR4HtjVb1jGX2IyMxtc0S8xFTnqcBS4TtJ+SWPA7cDhjjaHgQ+lt38WeMzj7WZmw5M7LJOOod8FPEoyFfLBiHhS0n3AZEQcBn4H+F1Jx4GXST4AzMxsSAqNuUfEEeBIx333Zm7PAj+3vKWZmdml8mRQM7M1yOFuZrYGOdzNzNYgh7uZ2RrkcDczW4OGthKTpCng+5f44ztZgVMbLAPXNRjXNbiy1ua6BvN66ro2InblNRpauL8ekiaLfENrtbmuwbiuwZW1Ntc1mNWoy8MyZmZrkMPdzGwNqmq4X3QGtJJwXYNxXYMra22uazArXlclx9zNzKy/qvbczcysj9KHu6SrJX1F0jFJT0r6aHr/DklfkvTn6fUbSlLXJySdkvREevnrq1zXuKT/K+kbaV2/nt6/X9LXJB2X9Hvp6ZvLUNd/kPS9zP66YTXrytRXl/R1SX+Ubg91f/Wpa+j7S9Kzkr6Vvv5ket9Q34996hrq+zGt4TJJj0j6jqSnJL17NfZX6cMdaAD/JCIOAO8CPiLpAHA38OWIuA74crpdhroAPh0RN6SXI72fYkXMAe+PiB8BbgBulvQukkXLPx0RPwS8QrKoeRnqAvjVzP56YpXravso8FRme9j7q62zLijH/vor6eu3p/MN+/3Yqy4Y7vsR4DPAH0fE24AfIfn3XPH9Vfpwj4jnIuLP0ttnSXbMHpJFuT+fNvs88DdKUtdQReJcujmaXgJ4P8ni5TCc/dWrrqGTtBf4KeCBdFsMeX91q6vkhvp+LCtJ24H3kqx5QURciIhXWYX9Vfpwz5K0D7gR+BpwZUQ8lz70PEuX3BxmXQB3SfqmpAeH9N/TuqQngBeBLwHfBV6NiEba5CRD+CDqrCsi2vvrX6X769OSNqx2XcC/Az4GC6slX04J9leXutqGvb8C+BNJjytZFxnK8X7sVhcM9/24H5gCPpcOrz0gaTOrsL8qE+6StgD/GfjHETGdfSxd0m8ovcAudX2WZNn2G4DngH+72jVFRDMibgD2AjcBb1vtGrrprEvS24F7SOr7MWAH8PHVrEnSTwMvRsTjq/m6efrUNdT9lfrLEfEO4BaS4cj3Zh8c4vuxW13Dfj+OAO8APhsRN5Ks5b1kCGal9lclwl3SKEmAfiEi/iC9+wVJu9PHd5P0BodeV0S8kIZYC/htknAdivS/f18B3g1cpmTxckjC9VQJ6ro5Hd6KiJgDPsfq768fB26V9CzwEMlwzGcY/v66qC5J/6kE+4uIOJVevwj8YVrD0N+P3eoqwfvxJHAy87/UR0jCfsX3V+nDPR3//B3gqYj4VOah7KLcHwL+axnqav+Dpf4m8O1VrmuXpMvS2xuBD5IcD/gKyeLlMJz91a2u72T+wEUy7riq+ysi7omIvRGxj2Tt38ci4u8w5P3Vo65fGPb+krRZ0tb2beCvpTUM+/3Yta5hvx8j4nnghKS3pnf9VeAYq7C/Cq2hOmQ/Dvxd4FvpeC3APwN+A3hY0odJzi75t0pS1x3p9LQAngV+aZXr2g18XlKd5MP74Yj4I0nHgIck/Uvg66QHeEpQ12OSdgECngB+eZXr6uXjDHd/9fKFIe+vK4E/TD5bGAG+GBF/LOkow30/9qrrd4f8fgT4hyT/bmPAM8DfJ30PrOT+8jdUzczWoNIPy5iZ2eAc7mZma5DD3cxsDXK4m5mtQQ53M7M1yOFuZrYGOdzNzNYgh7uZ2Rr0/wGRSYUq9diHfwAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Particle filter simulation\n", "V = np.arange(20, 60.1, .25)\n", "P_V = norm.pdf(V, loc=40., scale=5)\n", "P_V = P_V / P_V.sum() # So that altogether it equals 1\n", "\n", "P_SP = norm.pdf(V, loc=45, scale=5)\n", "P_SP = P_SP / P_SP.sum()\n", "\n", "for n in range(1000):\n", " \n", " sp = norm.rvs(loc=45, scale=5)\n", " P_V = L(sp) * P_V\n", " P_V = P_V / P_V.sum()\n", " \n", " if n % 50 == 0:\n", " plt.plot(V, P_V)\n", " plt.plot(V, P_SP)\n", " plt.vlines(45, 0, P_V[25*4], color='red')\n", " plt.draw()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(43.0, 47.0)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(V, P_V)\n", "plt.vlines(45, 0, .51, color='red')\n", "plt.xlim(43, 47)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }