Stock Price Distributions with Stochastic Volatility: An Analytic Approach

Elias M. Stein; Jeremy C. Stein

doi:10.1093/rfs/4.4.727

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Stock Price Distributions with Stochastic Volatility: An Analytic Approach

Elias M. Stein¹; Jeremy C. Stein²

¹ Princeton University · ² Massachusetts Institute of Technology

Review of Financial Studies 1991

We study the stock price distributions that arise when prices follow a diffusion process with a stochastically varying volatility parameter. We use analytic techniques to derive an explicit closed-form solution for the case where volatility is driven by an arithmetic Ornstein–Uhlenbeck (or AR1) process. We then apply 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 the nature of “fat tails” in stock price distributions.

DOI: 10.1093/rfs/4.4.727
Volume: 4 (4)
Pages: 727-752
Language: en
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