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Dynamic programming for valuing American options under a variance‐gamma process

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  • Hatem Ben‐Ameur
  • Rim Chérif
  • Bruno Rémillard

Abstract

Lévy processes provide a solution to overcome the shortcomings of the lognormal hypothesis. A growing literature proposes the use of pure‐jump Lévy processes, such as the variance‐gamma (VG) model. In this setting, explicit solutions for derivative prices are unavailable, for instance, for the valuation of American options. We propose a dynamic programming approach coupled with finite elements for valuing American‐style options under an extended VG model. Our numerical experiments confirm the convergence and show the efficiency of the proposed methodology. We also conduct a numerical investigation that focuses on American options on S&P 500 futures contracts.

Suggested Citation

  • Hatem Ben‐Ameur & Rim Chérif & Bruno Rémillard, 2020. "Dynamic programming for valuing American options under a variance‐gamma process," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(10), pages 1548-1561, October.
    • Handle: RePEc:wly:jfutmk:v:40:y:2020:i:10:p:1548-1561
    DOI: 10.1002/fut.22148
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    References listed on IDEAS

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