Pricing Options When Asset Return Follows a ''Colored'' Brownian Process
AMS Annual Meeting Proceedings, March 1996
Posted: 23 Aug 2010
Date Written: March 1, 1996
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
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