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Small-Time smile for the multifactor volatility heston model

Part of: Approximations and expansions Mathematical finance Limit theorems

Published online by Cambridge University Press:  23 November 2020

Dohyun Ahn ,
Kyoung-Kuk Kim  and
Younghoon Kim
Dohyun Ahn*
Affiliation:
The Chinese University of Hong Kong
Kyoung-Kuk Kim*
Affiliation:
Korea Advanced Institute of Science and Technology
Younghoon Kim*
Affiliation:
University of North Carolina at Chapel Hill
*
*Postal address: Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
**Postal address: Department of Industrial and Systems Engineering, KAIST, Daejeon, South Korea. Email address: kkim3128@kaist.ac.kr
***Postal address: Department of Statistics & Operations Research, University of North Carolina, Chapel Hill, NC, USA
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Abstract

We extend the existing small-time asymptotics for implied volatilities under the Heston stochastic volatility model to the multifactor volatility Heston model, which is also known as the Wishart multidimensional stochastic volatility model (WMSV). More explicitly, we show that the approaches taken in Forde and Jacquier (2009) and Forde, Jacqiuer and Lee (2012) are applicable to the WMSV model under mild conditions, and obtain explicit small-time expansions of implied volatilities.

Keywords

Implied volatilityWishart processasymptotic expansionlarge deviationLaplace expansion

MSC classification

Primary: 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Secondary: 60F10: Large deviations 91G60: Numerical methods (including Monte Carlo methods)
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1070 - 1087
Copyright
© Applied Probability Trust 2020

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