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Residue Sum Formula for Pricing Options under the Variance Gamma Model

Author

Listed:
  • Pedro Febrer

    (ISEG—School of Economics and Management, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, Portugal)

  • João Guerra

    (ISEG—School of Economics and Management, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, Portugal
    REM—Research in Economics and Mathematics, CEMAPRE, Rua do Quelhas 6, 1200-781 Lisboa, Portugal)

Abstract

We present and prove a triple sum series formula for the European call option price in a market model where the underlying asset price is driven by a Variance Gamma process. In order to obtain this formula, we present some concepts and properties of multidimensional complex analysis, with particular emphasis on the multidimensional Jordan Lemma and the application of residue calculus to a Mellin–Barnes integral representation in C 3 , for the call option price. Moreover, we derive triple sum series formulas for some of the Greeks associated to the call option and we discuss the numerical accuracy and convergence of the main pricing formula.

Suggested Citation

  • Pedro Febrer & João Guerra, 2021. "Residue Sum Formula for Pricing Options under the Variance Gamma Model," Mathematics, MDPI, vol. 9(10), pages 1-29, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1143-:d:557230
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    References listed on IDEAS

    as
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