Closed-Form Approximations for Spread Options in Lévy Markets

Abstract

We provide new closed-form approximations for the pricing of spread options in three specific instances of exponential Lévy markets, i.e., when log-returns are modeled as Brownian motions (Black-Scholes model), Variance Gamma processes (VG model) or Normal Inverse Gaussian processes (NIG model). For the specific case of exchange options (spread options with zero strike), we generalize the well-known Margrabe formula (1978) that is valid in a Black-Scholes model to the VG model under a homogeneity assumption.

Keywords: Stochastic Clock, Lévy Markets, Conditional Expectation, Gaussian Quadrature, Margrabe’s Formula