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A Finite Difference Method For The Valuation Of Variance Swaps

In: Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume III)

Author

Listed:
  • THOMAS LITTLE

    (Deutsche Bank AG, 31 West 52nd Street New York, NY 10019, USA)

  • VIJAY PANT

    (PricewaterhouseCoopers, 1177 Avenue of the Americas, New York, NY 10036, USA)

Abstract

We develop here a finite difference approach for valuing a discretely sampled variance swap within a Black-Scholes framework. This approach incorporates the observed volatility skew and is capable of handling various definitions of the variance. It is benchmarked against Monte-Carlo simulation in the presence of a volatility skew and is shown to provide extremely accurate values for a variance swap. Our method is based on decomposing the problem of valuing a variance swap into a set of one-dimensional PDE problems, each of which is then solved using a finite difference method.

Suggested Citation

  • Thomas Little & Vijay Pant, 2002. "A Finite Difference Method For The Valuation Of Variance Swaps," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume III), chapter 12, pages 275-295, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812778451_0012
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    Cited by:

    1. Yuecai Han & Xudong Zheng, 2022. "Approximate Pricing of Derivatives Under Fractional Stochastic Volatility Model," Papers 2210.15453, arXiv.org.
    2. Wang, Ke & Guo, Xun-xiang & Zhang, Hong-yu, 2024. "Valuations of generalized variance swaps under the jump–diffusion model with stochastic liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    3. Ke Wang & Xunxiang Guo, 2024. "Valuations of Variance and Volatility Swaps Under Double Heston Jump-Diffusion Model With Approximative Fractional Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 63(4), pages 1543-1573, April.

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    Keywords

    Quantitative Analysis; Financial Markets;

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