| Purdue Computational Finance Program | |
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Long Memory Stochastic Volatility
February 21, 2003 |
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Abstract:
Black and Scholes theory of option pricing assumes that the stock prices follows a geometric Brownian motion. The model has been generalized in many directions. One is to assume that the volatility is stochastic and follows a stochastic differential equation driven by Brownian motion. We shall consider the problem of option pricing and optimal consumption and portfolio when in the Black and Scholes market whe the the volatility is determined by a stochastic differential equation driven by fractional Brownian motion. |
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