{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "qORwXg8pWd2i", "pycharm": {} }, "source": [ "\n", "*This notebook contains course material from [CBE40455](https://jckantor.github.io/CBE40455) by\n", "Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE40455.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "KzKkNGpxWd2j", "pycharm": {} }, "source": [ "\n", "< [Geometric Brownian Motion](http://nbviewer.jupyter.org/github/jckantor/CBE40455/blob/master/notebooks/07.02-Geometric-Brownian-Motion.ipynb) | [Contents](toc.ipynb) | [Real Options](http://nbviewer.jupyter.org/github/jckantor/CBE40455/blob/master/notebooks/07.04-Real-Options.ipynb) >
"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "kM3RaIYhWd2j",
"pycharm": {}
},
"source": [
"# Binomial Model for Pricing Options\n",
"\n",
"This notebooks demonstrates techniques for pricing options using a binomial lattice to model prices of the underlying security or commodity. The notebook makes use of the pandas_datareader library to download pricing information, and the Pyomo modeling library for some example calculations.\n",
"\n",
" !pip install pandas_datareader"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "gJZ6RiMVWd2k",
"pycharm": {}
},
"source": [
"## Historical Data\n",
"\n",
"The first step is download historical data for a selected security or commodity. For the purposes of this notebook, it is useful to choose security of commodities for which there is an active options trading so the pricing model can be compared to real data.\n",
"\n",
"**Programming note:** Given a stock market symbol, the function ``yahoo_finance`` defined in the following cell creates a pandas data series object ``S`` of historical prices."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {},
"colab_type": "code",
"id": "z-lnCwIYWd2l",
"outputId": "e4df2555-b244-44e1-cb1d-08aa03ec8360",
"pycharm": {}
},
"outputs": [
{
"data": {
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3yClBEeYrc99Z3Mg3Xz0KEDInbKAoT5iipNFGQXosN8zP7lYZORDiTXqkhPYhfJa2nW3E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\nr1Ck+j3XJ6tbMWg1wdzNiamxbD5dT02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I8ViXpxKAkc9qBpqtTj77t/3sKWniq+tn8Pk1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\n8jMR6Xe7ImOSScWMfABe2z+yIcnDdU4vmE/67gk7UOMUYdP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"text/plain": [
" "
]
}
],
"metadata": {
"colab": {
"name": "07.03-Binomial-Model-for-Pricing-Options.ipynb",
"provenance": [],
"version": "0.3.2"
},
"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": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}