Stock Price Distributions with Stochastic Volatility: An Analytic Approach

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) proc...

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Bibliographic Details
Published inThe Review of financial studies Vol. 4; no. 4; pp. 727 - 752
Main Authors Stein, Elias M., Stein, Jeremy C.
Format Journal Article
LanguageEnglish
Published New York, NY Oxford University Press 01.01.1991
Published by Oxford University Press for the Society for Financial Studies
Oxford Publishing Limited (England)
Subjects
Approximation
Arithmetic
Infinity
Mathematical functions
Mathematical moments
Numerical analysis
Parametric models
Price volatility
Securities prices
Statistical variance
Stock market indices
Stock prices
Volatility
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0893-9454
1465-7368
DOI:10.1093/rfs/4.4.727