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Distributional Mellin calculus in $\mathbb{C}^n$, with applications to option pricing

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  • Jean-Philippe Aguilar
  • Cyril Coste
  • Hagen Kleinert
  • Jan Korbel

Abstract

We discuss several aspects of Mellin transform, including distributional Mellin transform and inversion of multiple Mellin-Barnes integrals in $\mathbb{C}^n$ and its connection to residue expansion or evaluation of Laplace integrals. These mathematical concepts are demonstrated on several option-pricing models. This includes European option models such as Black-Scholes or fractional-diffusion models, as well as evaluation of quantities related to the optimal exercise price of American options.

Suggested Citation

  • Jean-Philippe Aguilar & Cyril Coste & Hagen Kleinert & Jan Korbel, 2016. "Distributional Mellin calculus in $\mathbb{C}^n$, with applications to option pricing," Papers 1611.03239, arXiv.org, revised Nov 2016.
    • Handle: RePEc:arx:papers:1611.03239
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    Cited by:

    1. Jean-Philippe Aguilar & Cyril Coste & Hagen Kleinert & Jan Korbel, 2016. "Regularization and analytic option pricing under $\alpha$-stable distribution of arbitrary asymmetry," Papers 1611.04320, arXiv.org, revised Nov 2016.

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