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Pricing volatility swaps in the Heston’s stochastic volatility model with regime switching: A saddlepoint approximation method

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  • Mengzhe Zhang

    (School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia)

  • Leunglung Chan

    (School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia)

Abstract

Pricing a volatility swap is a highly nonlinear problem. Explicit solutions of the prices of volatility swaps are notoriously difficult to find. In this paper, we consider a saddlepoint approximation method for the valuation of a volatility swap under the Heston’s stochastic volatility model with regime switching. All the values of key parameters in our model are supposed to depend on the states of a continuous time observable Markov chain process. We present a closed-form exact cumulant generating functions (CGFs) of the continuous realized variance. Additionally, an approximated CGF is given. Then we approximate the volatility swaps by the saddlepoint approximation formula which derived from the Fourier inversion representation. The numerical results suggest that the alternative saddlepoint approximation method (ASAP) and the approximated ASAP method could both produce fairly accurate results for the given range of maturities.

Suggested Citation

  • Mengzhe Zhang & Leunglung Chan, 2016. "Pricing volatility swaps in the Heston’s stochastic volatility model with regime switching: A saddlepoint approximation method," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-20, December.
    • Handle: RePEc:wsi:ijfexx:v:03:y:2016:i:04:n:s2424786316500304
    DOI: 10.1142/S2424786316500304
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    References listed on IDEAS

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    Cited by:

    1. He, Xin-Jiang & Lin, Sha, 2023. "Analytically pricing variance and volatility swaps under a Markov-modulated model with liquidity risks," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).

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