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Stochastic Volatility in Mathematical Finance
Jan 17, 2001
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| Abstract: In the standard Black-Scholes model for a stock price as the solution to the so-called geometric Brownian motion equation, the random variations are assumed to be due to a white-noise factor whose intensity, called the volatility, is assumed to be constant. This is a very strong assumption on the future probabilistic behavior of the stock. It is a notorious fact that no stock price or worthy of that name is close to satisfying such an assumption for any significant length of time. We will review some of the models used in the literature to account for the fact that the volatility is not constant, concentrating on those models that allow it to be random itself, including the so-called ARCH/GARCH models, some stochastic volatility models, the relations between these models, and some applications we are in the process of developing with regards to portfolio optimization. |
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2001 Purdue University Last Update: July 10, 2001 Please send comments and suggestions to the Webmaster. |