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Variance Swap Pricing under Markov-Modulated Jump-Diffusion Model

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  • Shican Liu
  • Yu Yang
  • Hu Zhang
  • Yonghong Wu
  • Giancarlo Consolo

Abstract

This paper investigates the pricing of discretely sampled variance swaps under a Markov regime-switching jump-diffusion model. The jump diffusion, as well as other parameters of the underlying stock’s dynamics, is modulated by a Markov chain representing different states of the market. A semi-closed-form pricing formula is derived by applying the generalized Fourier transform method. The counterpart pricing formula for a variance swap with continuous sampling times is also derived and compared with the discrete price to show the improvement of accuracy in our solution. Moreover, a semi-Monte-Carlo simulation is also presented in comparison with the two semi-closed-form pricing formulas. Finally, the effect of incorporating jump and regime switching on the strike price is investigated via numerical analysis.

Suggested Citation

  • Shican Liu & Yu Yang & Hu Zhang & Yonghong Wu & Giancarlo Consolo, 2021. "Variance Swap Pricing under Markov-Modulated Jump-Diffusion Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-16, January.
    • Handle: RePEc:hin:jnddns:9814605
    DOI: 10.1155/2021/9814605
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