Pricing Options When Asset Return Follows a ''Colored'' Brownian Process

AMS Annual Meeting Proceedings, March 1996

Posted: 23 Aug 2010

See all articles by Steven H. Zhu

Steven H. Zhu

Banc of America Merrill Lynch; Morgan Stanley

Date Written: March 1, 1996

Abstract

The evolution of prices in market is usually given by geometric Brownian motion, where the Brownian process describes fluctuations is often called "white" noise. We study the effect of correlations introduced by a "colored" noise.

We demonstrate how the "color" Brownian process may capture the momentum often observed in the market prices. When the prices follow the "colored" Brownian process, we show the price of option can be obtained explicitly as a solution to the generalized Fokker-Planck equation.

Keywords: Brownian Motion, Colored Noise, Option Pricing and Fokker-Planck Equation

Suggested Citation

Zhu, Steven H., Pricing Options When Asset Return Follows a ''Colored'' Brownian Process (March 1, 1996). AMS Annual Meeting Proceedings, March 1996. Available at SSRN: https://ssrn.com/abstract=1663383

Steven H. Zhu (Contact Author)

Banc of America Merrill Lynch ( email )

Bank of America Plaza
335 Madison Ave, 5th Floor
New York, NY 10017
United States
646-855-1853 (Phone)

HOME PAGE: http://www.riskwhoswho.com/Charter-Members.html

Morgan Stanley ( email )

1585 Broadway
New York, NY 10036
United States

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