{ "cells": [ { "cell_type": "markdown", "id": "ccfa6344", "metadata": {}, "source": [ "# Ornstein-Uhlenbeck Model" ] }, { "cell_type": "markdown", "id": "109a4920", "metadata": {}, "source": [ "In finance, the OU process is often used to model the evolution of a commoditiy's price over time. In this context, the OU process is used to capture the tendency of prices to return to their long-term average, while allowing for random fluctuations around that average.\n", "\n", "$$ dX_t = \\lambda(\\mu-X)dt++\\sigma dW_t. $$\n", "\n", "Here\n", "\n", "- $\\lambda$ is the speed of mean reversion and determines how fast the process drifts to the mean reversion level $\\mu$,\n", "- $\\mu$ denotes the mean reversion level,\n", "- $\\sigma$ is the volatiity of the process.\n", "\n", "The OU model has several properties that make it useful for modeling real-world phenomena. For example, it is a stationary process, meaning that its statistical properties do not change over time. It is also Markovian, meaning that its future behavior depends only on its current state, not on its past history." ] }, { "cell_type": "code", "execution_count": 6, "id": "6336d9b3", "metadata": { "ExecuteTime": { "end_time": "2023-05-11T05:25:08.960463Z", "start_time": "2023-05-11T05:25:04.296785Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/doeltz/doeltz/development/RiVaPy/rivapy/__init__.py:11: UserWarning: The pyvacon module is not available. You may not use all functionality without this module. Consider installing pyvacon.\n", " warnings.warn('The pyvacon module is not available. You may not use all functionality without this module. Consider installing pyvacon.')\n", "2023-05-11 07:25:05.860283: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcudart.so.11.0'; dlerror: libcudart.so.11.0: cannot open shared object file: No such file or directory\n", "2023-05-11 07:25:05.860298: I tensorflow/stream_executor/cuda/cudart_stub.cc:29] Ignore above cudart dlerror if you do not have a GPU set up on your machine.\n" ] } ], "source": [ "import sys\n", "sys.path.append('../../../..')\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import rivapy" ] }, { "cell_type": "markdown", "id": "4fa85cf9", "metadata": {}, "source": [ "## Simulation of Spot" ] }, { "cell_type": "code", "execution_count": 17, "id": "3bbda761", "metadata": { "ExecuteTime": { "end_time": "2023-05-11T05:28:39.140055Z", "start_time": "2023-05-11T05:28:36.327259Z" }, "tags": [ "nbsphinx-thumbnail" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rnd = np.random.normal(size=(timegrid.shape[0],10_000))\n", "plt.figure(figsize=(16,4))\n", "for mr_speed, volatility in [(10.0,0.3), (0.1,0.3), (10.0, 1.0), (0.1,1.0)]:\n", " ou_model = rivapy.models.OrnsteinUhlenbeck(speed_of_mean_reversion = mr_speed, volatility=volatility)\n", " sim = ou_model.simulate(timegrid, start_value=0.0, rnd=rnd)\n", " plt.subplot(1,2,1)\n", " plt.plot(timegrid,sim[:,0],'-', label='$\\lambda$='+str(mr_speed)+', $\\sigma$=' + str(volatility))\n", " plt.xlabel('time [years]')\n", " plt.legend()\n", " plt.subplot(1,2,2)\n", " plt.hist(sim[-1,:], bins=100, density=True, alpha=0.25,\n", " label='$\\lambda$='+str(mr_speed)+', $\\sigma$=' + str(volatility))\n", " plt.legend('simulated value at final time')\n", " plt.legend()" ] }, { "cell_type": "markdown", "id": "43f1b7d2", "metadata": {}, "source": [ "## Calibration" ] }, { "cell_type": "markdown", "id": "67252b4e", "metadata": {}, "source": [ "The model may be calibrated to data. Here, the data must be given on a uniform grid. The calibration can either be done by maximum likelihood or by minimum least square.\n", "\n", "Here, to test the calibration, we simulate paths of an Ornstein-Uhlenbeck process and calibrate to this simulated data." ] }, { "cell_type": "code", "execution_count": 18, "id": "781c6376", "metadata": { "ExecuteTime": { "end_time": "2023-05-11T05:28:47.944388Z", "start_time": "2023-05-11T05:28:45.878619Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "timegrid = np.arange(0.0,5.0,1.0/365.0) # simulate on daily timegrid over 5yrs horizon\n", "\n", "iters = 100 # number of calibrations performed on simualted data\n", "mean_reversion_speed, volatility, mean_level = np.empty((iters,)), np.empty((iters,)), np.empty((iters,))\n", "\n", "for i in range (iters):\n", " ou_model = rivapy.models.OrnsteinUhlenbeck(speed_of_mean_reversion = 5.0, volatility=0.1)\n", " sim = ou_model.simulate(timegrid, start_value=0.2,rnd=np.random.normal(size=(timegrid.shape[0],1)))\n", " ou_model.calibrate(sim.reshape((-1)),dt=1.0/365.0, method = 'minimum_least_square')\n", " mean_reversion_speed[i] = ou_model.speed_of_mean_reversion\n", " volatility[i] = ou_model.volatility\n", " mean_level[i] = ou_model.mean_reversion_level\n", " \n", "plt.figure(figsize=(16,6))\n", "plt.subplot(1,3,1)\n", "plt.hist(mean_reversion_speed, bins=10)\n", "plt.title('speed of meanreversion')\n", "plt.xlabel('speed of meanreversion')\n", "plt.subplot(1,3,2)\n", "plt.hist(volatility, bins=10)\n", "plt.title('volatility')\n", "plt.xlabel('volatility')\n", "plt.subplot(1,3,3)\n", "plt.hist(mean_level, bins=10)\n", "plt.title('mean reversion level')\n", "plt.xlabel('mean reversion level');" ] }, { "cell_type": "code", "execution_count": null, "id": "0939f3d7", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Tags", "hide_input": false, "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" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "165px" }, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 5 }