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Asymptotic Expansion Formula of Option Price Under Multifactor Heston Model

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  • Kazuki Nagashima
  • Tsz-Kin Chung
  • Keiichi Tanaka

Abstract

The stochastic volatility model of Heston (Rev Financ Stud 6(2):327–343, 1993 ) has found difficulty in describing some of the important features of implied volatility dynamics, leading to a quest for multifactor extensions as well as the incorporation of time-dependent model parameters. In this paper, an asymptotic expansion approach to the multifactor Heston model with time-dependent parameters is developed. The results of Benhamou et al. (SIAM J Financ Math 1(1):289–325, 2010 ) are extended and it is shown that the extension to the multifactor model involves an extra expansion term that captures the interaction between variance factors. The expansion formula under constant parameters can be explicitly computed and the incorporation of time-dependent parameters is straightforward under the framework. As illustration, a two-factor model is calibrated to data of index options and variance swaps and it is found that it is possible to distinguish a short-term and long-term variance factor from the implied volatility surface and variance swap rates. Moreover, the two-factor model is able to reproduce the shapes of the implied volatility surface during various market scenarios. Copyright Springer Japan 2014

Suggested Citation

  • Kazuki Nagashima & Tsz-Kin Chung & Keiichi Tanaka, 2014. "Asymptotic Expansion Formula of Option Price Under Multifactor Heston Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 351-396, November.
    • Handle: RePEc:kap:apfinm:v:21:y:2014:i:4:p:351-396
    DOI: 10.1007/s10690-014-9189-4
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    References listed on IDEAS

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    Cited by:

    1. Choi, Sun-Yong, 2019. "The influence of shock signals on the change in volatility term structure," Economics Letters, Elsevier, vol. 183(C), pages 1-1.
    2. Yanhong Zhong & Guohe Deng, 2019. "Geometric Asian Options Pricing under the Double Heston Stochastic Volatility Model with Stochastic Interest Rate," Complexity, Hindawi, vol. 2019, pages 1-13, January.
    3. Recchioni, Maria Cristina & Iori, Giulia & Tedeschi, Gabriele & Ouellette, Michelle S., 2021. "The complete Gaussian kernel in the multi-factor Heston model: Option pricing and implied volatility applications," European Journal of Operational Research, Elsevier, vol. 293(1), pages 336-360.

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