TITLE:
Financial Modeling with Geometric Brownian Motion
AUTHORS:
Chelsea Peng, Colette Simon
KEYWORDS:
Stochastic Calculus, Geometric Brownian Motion, Financial Modeling
JOURNAL NAME:
Open Journal of Business and Management,
Vol.12 No.2,
March
28,
2024
ABSTRACT: This project evaluates Brownian Motion’s
effectiveness compared to historical stock market data. This paper analyzes the
application and limitations of this stochastic model, focusing on the Dow Jones
Industrial Average (DJIA) to evaluate its accuracy in predicting stock market
trends. The paper begins by tracing the historical context of stochastic
calculus, highlighting the contributions of Louis Bachelier and Albert Einstein
in laying the foundation for modern financial modeling. Geometric Brownian
Motion (GBM) is then introduced with options pricing and then examined through
the lens of the Markov property, emphasizing its “memoryless” nature. To test
this, simulations were coded using Python simulations of the DJIA Index, based
on Brownian Motion across the periods 1900-2000 and 2000-2015. These models
were then compared to the actual historical data of the DJIA to evaluate
predictive validity. Stochastic elements reflect factors that influence the
value of a derivative, like time, volatility of the underlying asset, interest
rates, and other market conditions. The research also critically examines the
model’s inherent limitations, aiming to provide insights into the extent to
which GBM can be a reliable tool for financial forecasting. This comparison
will enable a nuanced understanding of the utility and shortcomings of this
model for economic predictions and stock market analysis.