Stock price distributions with stochastic volatility: an analytic approach |
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Authors: | Stein, EM Stein, JC |
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Affiliation: | 1 Princeton University, Princeton, USA 2 Sloan School of Management, MIT, Cambridge, MA 02139, USA |
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Abstract: | We study the stock price distributions that arise when pricesfollow a diffusion process with a stochastically varying volatilityparameters. We use analytic techniques to derive an explicitclosed-form solution for the case when volatility is drivenby an arithmetic Ornstein-Uhlenbeck (or AR1) process. We thenapply our results to two related problems in the finance literature:(i) options pricing in a world of stochastic volatility, and(ii) the relationship between stochastic volatility and thenature of 'fat tails' in stock price distributions. |
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