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@FilippoGuerrieri26
Created July 12, 2023 18:27
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GBM
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"# Geometric Brownian Motion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Geometric Brownian Motion is a continuous-time stohastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (or Wiener process) with drift. <br>\n",
"The GMB formula <br>\n",
"<br>\n",
"$ dS_t = \\mu S_tdt + \\sigma S_tdW_t $ <br>\n",
"<br>\n",
"$ W_t $ is a Wiener Process <br>\n",
"$ \\mu $ and $ \\sigma $ are constant <br>\n",
"<br>\n",
"The first parameter is meant to model the deterministic trend, while the second parameter models the unpredictable component"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Montecarlo Simulation of GMB"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Import packages\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import ipywidgets as widgets\n",
"from IPython.display import display"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Code GMB"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
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"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
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"\n",
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"\n",
" .dataframe thead th {\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>0</th>\n",
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" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>100.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>98.696888</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>97.879039</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>97.845119</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>97.193537</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
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" <tr>\n",
" <th>1256</th>\n",
" <td>109.336999</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1257</th>\n",
" <td>109.496546</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1258</th>\n",
" <td>110.187574</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1259</th>\n",
" <td>109.331283</td>\n",
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"<p>1261 rows × 1 columns</p>\n",
"</div>"
],
"text/plain": [
" 0\n",
"0 100.000000\n",
"1 98.696888\n",
"2 97.879039\n",
"3 97.845119\n",
"4 97.193537\n",
"... ...\n",
"1256 109.336999\n",
"1257 109.496546\n",
"1258 110.187574\n",
"1259 109.331283\n",
"1260 109.558199\n",
"\n",
"[1261 rows x 1 columns]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Define inputs and simulate returns\n",
"s_0 = 100.0 # initial price at t0\n",
"mu = 0.05 # fist moment of the distribution (average)\n",
"sigma = 0.10 # second moment of the distribution (std)\n",
"steps_per_year = 252 # frequency of the data to be simulated. In this case, daily\n",
"n_years = 5 # number of years to be simulated\n",
"n_scenarios = 1 # number of simulations\n",
"prices = True # this boolean variable is used to decide whether spit out prices or returns\n",
"\n",
"dt = 1 / steps_per_year\n",
"n_steps = int(n_years * steps_per_year) + 1\n",
"ret_1 = np.random.normal(loc=(1 + mu)**dt, # annualized drift\n",
" scale=(sigma * np.sqrt(dt)), # annualized variance\n",
" size=(n_steps, n_scenarios)) # shape: number of values and scenarios\n",
"ret_1[0] = 1 # setting initial return to 1\n",
"ret_val = s_0 * pd.DataFrame(ret_1).cumprod() if prices else pd.DataFrame(ret_1 - 1) # compute prices if True, else just returns\n",
"\n",
"ret_val"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 0, 'Step')"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1296x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Plot our simulation\n",
"plt.figure(figsize=(18, 8))\n",
"plt.plot(ret_val)\n",
"plt.title(\"Simulated stock price\")\n",
"plt.grid()\n",
"plt.ylabel(\"Price\")\n",
"plt.xlabel(\"Step\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Define GBM Function"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"def geometric_brownian_motion(s_0, n_years, steps_per_year, mu, sigma, n_scenarios, convert_to_prices=True):\n",
" dt = 1 / steps_per_year\n",
" n_steps = int(n_years * steps_per_year) + 1\n",
" rets_plus_1 = np.random.normal(loc=(1 + mu)**dt, scale=(sigma * np.sqrt(dt)), size=(n_steps, n_scenarios))\n",
" rets_plus_1[0] = 1\n",
" ret_val = s_0 * pd.DataFrame(rets_plus_1).cumprod() if convert_to_prices else rets_plus_1-1\n",
" return ret_val"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. Define interactive function to be displayed using pywidget"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"def show_gbm(s_0=100.0, n_years=10, steps_per_year=12, mu=0.05, sigma=0.10, n_scenarios=5):\n",
" geometric_brownian_motion(s_0=s_0, n_years=n_years, steps_per_year=steps_per_year,\n",
" mu=mu, sigma=sigma, n_scenarios=n_scenarios).plot(legend=False, figsize=(18, 8))\n",
" plt.title(\"Simulated Stock Price Paths \\nNumber of simulations: {} \\nmu: {}% sigma: {}%\".format(n_scenarios,\n",
" mu * 100,\n",
" sigma * 100))\n",
" plt.ylabel(\"Price\")\n",
" plt.xlabel(\"Step\")\n",
" plt.grid()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4. Pywidget GBM Simulation"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "18910d8bc58d4e41ab05d73c4a53820b",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(IntSlider(value=100, description='s_0', max=300, min=-100), IntSlider(value=10, descript…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"controls = widgets.interactive(show_gbm,\n",
" s_0 = 100,\n",
" n_years = (0, 30, 1),\n",
" steps_per_year = (12, 252, 1),\n",
" mu = (0, .1, 0.01),\n",
" sigma= (0, .1, .01),\n",
" n_scenarios = (1, 100))\n",
"display(controls)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"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": "3.9.12"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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