Modeling Stock Price Dynamics, using Stochastic Differential Equation

Abstract

In this notebook, I built a stochastic differential equation in Python which is commonly used for modeling and predicting asset price dynamics. I explained and built with Python basic concepts such as Random Walk and Wiener process (Brownian motion). These were needed to build the Geometric Brownian Motion model which is one of a few stochastic differential equations that has a closed-form solution. For the exact GBM model, I used Alphabet Inc. (GOOGL) share prices, which were extracted from Quandl. In the end, Euler-Maruyama approximation was used to verify our model against the closed-form solution.

I am pretty sure my EM approximation is not written correctly with Python code, so I would appreciate contributions and suggestions for this work.