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

Mengzhe Zhang () and Leunglung Chan ()
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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

International Journal of Financial Engineering (IJFE), 2016, vol. 03, issue 04, 1-20

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.

Keywords: Volatility swap; Markov-modulated geometric Brownian motion; regime switching model; saddlepoint approximation method; stochastic volatility model (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S2424786316500304

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