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Zhenyu Cui: Probability Density, Implied Volatility and Timer Options in Stochastic Volatility Models

Submitted by Andreas L. Freund on April 14, 2016 - 11:00am

Speaker: Zhenyu Cui, Stevens Institute of Technology

Date: April 14, 2016

Title: Probability Density, Implied Volatility and Timer Options in Stochastic Volatility Models

Abstract: We describe a generic probabilistic method to derive explicit exact probability density functions for stochastic volatility models. Our method is based on a novel application of the exponential measure change in Palmowski and Rolski (2002). With this generic method, we first derive explicit exact probability densities in terms of model parameters for five popular stochastic volatility models with non-zero correlation, namely the Heston, Hull-White, 3/2, 4/2 and alpha-hypergeometric stochastic volatility models. Next, we combine the probability densities, the “mixing approach” of Romano and Touzi (1996), and a representation of the implied volatility surface to obtain explicit exact formulae for European call options and the corresponding implied volatilities for these five models in terms of model parameters. Finally, we apply our generic probabilistic method to develop explicit exact formulae for prices of timer options in Heston, 3/2 and alpha-hypergeometric models.

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