Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models

By Archil Gulisashvili, E. Stein. 2009

60 citations recorded by the source corpus.

We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model. We find explicit formulas for leading terms in asymptotic expansions of these densities and give error estimates. As an application of our results, sharp asymptotic formulas for the implied volatility in the Stein-Stein and the Heston model are obtained.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/90907b91e82bb3e4e774a123675cbcf8ba945e41

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In Mathematical Physics

Citations in the corpus

Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations (2011, background): “First, as was already mentioned, c2 D 0 in these works, whereas expansions with c2 ¤ 0 are crucial in understanding the tail behavior of certain stochastic volatility models [12] (see also [14, 19]).”
Asymptotic formulae for implied volatility in the Heston model (2009, background): “For instance, the SABR stochastic volatility model has become very popular because a closed-form approximation formula for the implied volatility was derived in Hagan et al. (2002) and hence made the model easily tractable.”