Geometric Brownian Motion Simulation for Stock Price Modeling: Report

This report analyzes the application of Geometric Brownian Motion (GBM) in modeling stock prices. It highlights the importance of the drift component, representing the expected return, and its impact on simulated stock prices. The report emphasizes the need to verify that a time series follows the GBM process and discusses the two components of GBM: the certain component (expected return or drift) and the uncertain component (volatility). It also references sources that explore the relationship between drift, volatility, and simulated stock prices. The report uses Monte Carlo simulations to model stock prices and discusses the stochastic nature of the process. The analysis includes insights from relevant literature and research.

REPORT SUMMARY
Given a geometric Brownian motion for modelling a stock price a monte
Carlo simulation to stochastically model stock prices for a given asset. The
component of drift is the component used to determine the expected return
in the stochastic model, hence it is the direct function.
The stock price is expected to drift in opposite directions depending on the
returns. It is also important to verify that a time series follows the geometric
Brownian motion process assumed (Marathe & Ryan, 2005).
According to Sengupta (2004) GBM has two components that include the
following certain component and uncertain component, the certain attribute
the expected return earned by the stock over a short period of time which is
represented as the drift of the stock. While the uncertain component is
composed of the stochastic process that includes the volatility of stocks and
the aspect of volatility that is random.
According to Brewer,et.al (2012) any Brownian motion simulations both the
drift and the parameter of volatility are important and a higher drift value
tends to result in higher simulated prices over the period being analyzed.
REFERENCES
Brewer, K., Feng, Y., & Kwan, C. (2012). Geometric Brownian motion, option
pricing, and simulation: some spreadsheet-based exercises in financial
modelling. Spreadsheets in Education, 5(3), article 4. Retrieved from
http://epublications.bond.edu.au/ejsie/
Marathe, R., & Ryan, S. (2005). One the validity of the geometric Brownian
motion assumption. The Engineering Economist: A Journal Devoted to
the Problems of Capital Investment, 50(2), 159- 192.
http://dx.doi.org/10.1080/00137910590949904
Sengupta, C. (2004). Financial modelling using Excel and VBA. New Jersey,
United States: John Wiley & Sons.