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

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.

v1-2: more details on the American option part, some references added, 23 pages, 3 figures

References in corpus (2)

• Analytical properties and applications of the Wright function
• Muon Anomaly from Lepton Vacuum Polarization and The Mellin--Barnes Representation