{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Stock price modelling for the mathematically curious\n", "\n", "In this notebook we discuss a mathematical model for stock prices. We present some numerical approximations and illustrate these with simple plots." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bank balance as an Ordinary Differential Equation\n", "\n", "Consider the general ordinary differential equation for unknown $U : (0,\\infty) \\to \\mathbb{R}$,\n", "\n", "$$\n", "\\tag{ODE}\n", "\\frac{dU(t)}{dt} = f(t,U(t)), \\quad t > 0,\n", "$$\n", "\n", "with a given initial value $U(0) = U_0$ and function $f : (0,\\infty) \\times \\mathbb{R} \\to \\mathbb{R}$.\n", "\n", "By integrating, we see that it is equivalent with the integral equation\n", "\n", "$$\n", "\\tag{IE}\n", "U(t) = U_0 + \\int_0^t f(s,U(s)) \\, ds , \\quad t > 0.\n", "$$\n", "\n", "For example, we could be modelling our bank account balance $B$ by\n", "\n", "$$\n", "\\frac{dB(t)}{dt} = \\mu B(t) + F(t), \\quad t > 0,\n", "$$\n", "\n", "where $\\mu$ is the interest rate and $F$ stands for, say, your salary or expenses.\n", "\n", "It is easy to see that the solution to this equation is given by\n", "\n", "$$\n", "B(t) = e^{\\mu t}B_0 + \\int_0^t e^{\\mu (t-s)} F(s) \\, ds , \\quad t > 0,\n", "$$\n", "\n", "where $B_0$ is the initial balance.\n", "\n", "Remark: For a bank account, a discrete model would probably be a more realistic choice, but we wish to emphasize the analogy between this and the continuous time model for stock price." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# We inspect our model over a time frame\n", "\n", "import pandas as pd\n", "import numpy as np\n", "\n", "start_date = '2017-01-01'\n", "end_date = '2017-12-31'\n", "date_range = pd.date_range(start=start_date, end=end_date)\n", "\n", "# We assume that the daily earnings and expenses vary somewhat randomly\n", "daily_earnings_avg = 10.0 # average daily earnings\n", "daily_expenses_scale = 50.0 # scale of unexpected expenses\n", "F_df = pd.DataFrame(data=np.random.normal(loc=daily_earnings_avg, \n", " scale=daily_expenses_scale, \n", " size=len(date_range)), \n", " index=date_range)\n", "\n", "def F(s):\n", " return F_df.loc[s].values\n", "\n", "B_0 = 10000 # Initial bank balance at 10000 euros\n", "mu = 0.01 / 365 # 1 percent annual interest rate transformed into daily interest rate\n", "\n", "def integrand(t,s):\n", " return np.exp(mu * (t - s).days) * F(s)\n", "\n", "def integral(t):\n", " return sum([integrand(t,s) for s in pd.date_range(start=start_date, end=t)])\n", "\n", "def B(t):\n", " return np.exp(mu * (t - pd.to_datetime(start_date)).days) * B_0 + integral(t)\n", "\n", "bank_balance = pd.DataFrame(data=[np.round(B(t),2) for t in date_range], index=date_range, columns=['bank_balance'])" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "