Non-Gaussian analytic option pricing: a closed formula for the Lévy-stable model

Abstract

We establish an explicit pricing formula for the class of Lévy-stable models with maximal negative asymmetry (Log-Lévy model with finite moments and stability parameter $1<\alpha \le 2$) in the form of rapidly converging series. The series is obtained with help of Mellin transform and the residue theory in ${\mathbb{C}}^2$. The resulting formula enables the straightforward evaluation of an European option with arbitrary accuracy without the use of numerical techniques. The formula can be used by any practitioner, even if not familiar with the underlying mathematical techniques. We test the efficiency of the formula, and compare it with numerical methods.

arXiv commentv2-2 (nov 17): theoretical details and other numerical tests added

References in corpus (4)

• Option Pricing Beyond Black-Scholes Based on Double-Fractional Diffusion
• Muon Anomaly from Lepton Vacuum Polarization and The Mellin--Barnes Representation
• Multiple Mellin-Barnes Integrals as Periods of Calabi-Yau Manifolds With Several Moduli
• Option Pricing from Path Integral for Non-Gaussian Fluctuations. Natural Martingale and Application to Truncated Lévy Distributions

Cited by in corpus (3)

• Option Pricing Models Driven by the Space-Time Fractional Diffusion: Series Representation and Applications
• Regularization and analytic option pricing under $\alpha$-stable distribution of arbitrary asymmetry
• Distributional Mellin calculus in ${\mathbb{C}}^n$, with applications to option pricing