Abstract
Though geometric Brownian motion (GBM) is an essential tool in finance, a closed form solution for its transition density function has yet to be obtained. In option pricing, though Black and Scholes assumed GBM stock price dynamics, they transformed the problem to allow an option to be evaluated without the stock price’s transition density. This paper presents a closed form solution of Kolmogorov’s backward equation for GBM. As an application, the option price equation is derived directly.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Black, F. & M. Scholes (1973). The Pricing of Options and Corporate Liabilities, J. Pol. Econ., 81, 637–654.
Kozin, F. (1972). Stability of the Linear Stochastic System, in R. Curtain ed., Stability of Stochastic Dynamical Systems, New York: Springer Verlag.
Samuelson, P. A. (1965). Rational Theory of Warrant Pricing, Industrial Management Rev., 6, 13–31.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cheung, M.T., Yeung, D., Lai, A. (1993). On the Use of Geometric Brownian Motion in Financial Analysis. In: Karmann, A., Mosler, K., Schader, M., Uebe, G. (eds) Operations Research ’92. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12629-5_149
Download citation
DOI: https://doi.org/10.1007/978-3-662-12629-5_149
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-0679-3
Online ISBN: 978-3-662-12629-5
eBook Packages: Springer Book Archive