Using pseudo-parabolic and fractional equations for option pricing in jump diffusion models

摘要

In mathematical finance a popular approach for pricing options under someLevy model is to consider underlying that follows a Poisson jump diffusionprocess. As it is well known this results in a partial integro-differentialequation (PIDE) that usually does not allow an analytical solution whilenumerical solution brings some problems. In this paper we elaborate a newapproach on how to transform the PIDE to some class of so-calledpseudo-parabolic equations which are known in mathematics but are relativelynew for mathematical finance. As an example we discuss several jump-diffusionmodels which Levy measure allows such a transformation.