Short-Maturity Asymptotics for a Fast Mean-Reverting Heston Stochastic Volatility Model | Zendy

Jin Feng | Zendy; Martin Forde | Zendy; JeanPierre Fouque | Zendy

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Short-Maturity Asymptotics for a Fast Mean-Reverting Heston Stochastic Volatility Model

Author(s) -

Jin Feng,

Martin Forde,

JeanPierre Fouque

Publication year - 2010

Publication title -

siam journal on financial mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.251

H-Index - 33

ISSN - 1945-497X

DOI - 10.1137/090745465

Subject(s) - mean reversion , stochastic volatility , heston model , mathematics , volatility (finance) , implied volatility , sabr volatility model , forward volatility , econometrics , asymptotic expansion , moment (physics) , economics , mathematical analysis , physics , classical mechanics

In this paper, we study the Heston stochastic volatility model in a regime where the maturity is small but large compared to the mean-reversion time of the stochastic volatility factor. We derive a large deviation principle and compute the rate function by a precise study of the moment generating function and its asymptotic. We then obtain asymptotic prices for out-of-the-money call and put options and their corresponding implied volatilities.

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