Valuing Bermudan options when asset returns are Lévy processes

Abstract

Evidence from the financial markets suggests that empirical returns distributions, both historical and implied, do not arise from diffusion processes. A growing literature models the returns process as a Lévy process, finding a number of explicit formulae for the values of some derivatives in special cases. Practical use of these models has been hindered by a relative paucity of numerical methods which can be used when explicit solutions are not present. In particular, the valuation of Bermudan options is problematical. This paper investigates a lattice method that can be used when the returns process is Lévy, based upon an approximation to the transition density function of the Lévy process. We find alternative derivations of the lattice, stemming from alternative representations of the Lévy process, which may be useful if the transition density function is unknown or intractable. We apply the lattice to models based on the variance-gamma and normal inverse Gaussian processes. We find that the lattice is able to price Bermudan-style options to an acceptable level of accuracy.