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On the Use of Geometric Brownian Motion in Financial Analysis

  • Michael Tow Cheung
  • David Yeung
  • Alfred Lai
Conference paper

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.

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References

  1. Black, F. & M. Scholes (1973). The Pricing of Options and Corporate Liabilities, J. Pol. Econ., 81, 637–654.CrossRefGoogle Scholar
  2. Kozin, F. (1972). Stability of the Linear Stochastic System, in R. Curtain ed., Stability of Stochastic Dynamical Systems, New York: Springer Verlag.Google Scholar
  3. Samuelson, P. A. (1965). Rational Theory of Warrant Pricing, Industrial Management Rev., 6, 13–31.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Michael Tow Cheung
    • 1
  • David Yeung
    • 1
  • Alfred Lai
    • 1
  1. 1.School of EconomicsUniversity of Hong KongHong KongHong Kong

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