{ "cells": [ { "cell_type": "markdown", "id": "acf9e9f0-2485-4a3e-8d87-3ce66ef29c1e", "metadata": {}, "source": [ "# Ito Processes\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demsoc00.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2021-Oct-01\n", "
" ] }, { "cell_type": "markdown", "source": [ "## Simulate geometric Brownian motion" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%% md\n" } } }, { "cell_type": "code", "execution_count": 1, "id": "d8850241-2309-4699-8853-37869d67794a", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.style.use('seaborn')" ] }, { "cell_type": "markdown", "id": "fef6b416-f893-42dc-9002-963d1a5fa6d8", "metadata": {}, "source": [ "## Model Parameters" ] }, { "cell_type": "code", "execution_count": 2, "id": "ff737e92-887a-4237-99bb-4a8af93fde2f", "metadata": {}, "outputs": [], "source": [ "T = 1\n", "n = 365\n", "t = np.linspace(0, T, n)\n", "h = t[1] - t[0]\n", "\n", "𝜇 = 0.1\n", "𝜎 = 0.05" ] }, { "cell_type": "markdown", "id": "2b07955d-48d8-407f-8bd3-ef29cdf5d2e4", "metadata": {}, "source": [ "## Simulate" ] }, { "cell_type": "code", "execution_count": 3, "id": "56d047ab-2af1-42bb-b234-10f604305c13", "metadata": {}, "outputs": [], "source": [ "m = 3\n", "z = np.random.randn(n,m)\n", "s = np.zeros((n,m))\n", "s[0] = 1\n", "for i in range(n-1):\n", " s[i+1] = s[i] + 𝜇*s[i]*h + 𝜎*s[i]*np.sqrt(h)*z[i]" ] }, { "cell_type": "markdown", "id": "84fff369-7770-43a2-ac54-38945a66900f", "metadata": {}, "source": [ "## Plot" ] }, { "cell_type": "code", "execution_count": 4, "id": "8edda032-aa2e-46c2-af36-53fe46ade5fb", "metadata": {}, "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=[8,4])\n", "ax.plot(t,s)\n", "ax.set(xlabel='$t$',\n", " ylabel='$s(t)$',\n", " title='Simulated Geometric Brownian Motion, $\\mu=0.1$, $\\sigma=0.05$');" ] }, { "cell_type": "code", "execution_count": 5, "id": "7b6c8bdb-1f93-4abf-8c5d-dcf03e63087b", "metadata": {}, "outputs": [], "source": [ "#fig.savefig('demsoc00-01.pdf', bbox_inches='tight')" ] } ], "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 5 }