bs01 return rates, instead of the stock prices, follow a Brownian motion (also known as the "geometric

Kendall (1953), Roberts (1959), Osborne (1959; 1964) and Samuelson (1965) modified the

Bachelier model (also known as the "arithmetic Brownian motion" model) assuming that the

return rates, instead of the stock prices, follow a Brownian motion (also known as the "geometric

Brownian motion" model or the "economic Brownian motion" model). 

STOCHASTIC MODELING OF STOCK PRICES
 Stochastic Modeling of Stock Prices

© Montgomery Investment Technology, Inc. / Sorin R. Straja, Ph.D., FRM
 May 1997


Sorin R. Straja, Ph.D., FRM
Montgomery Investment Technology, Inc.

200 Federal Street

Camden, NJ 08103

Phone: (610) 688-8111
sorin.straja@fintools.com

www.fintools.com
 

　
ABSTRACT


The geometric Brownian motion model is widely used to explain the stock price time series. The

following sections summarize its main features. The stochastic model may be viewed as an

extension of the usual deterministic model for which the rate of return is viewed as a constant

value subjected to perturbations. We present both the Ito and Stratonovich interpretations of the

resulting stochastic differential equation. The parameters estimation and model predictions

could be done using either interpretation; however, the same interpretation must be used for both

steps (i.e., parameters estimation and model predictions).