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

TL;DR

This paper introduces a novel method transforming complex PIDE equations in jump diffusion models into pseudo-parabolic equations, facilitating more effective option pricing analysis in mathematical finance.

Contribution

It presents a new approach to convert PIDEs into pseudo-parabolic equations for jump diffusion models, a technique not previously applied in finance.

Findings

Transforming PIDEs simplifies numerical solutions.

Applicable to several Levy jump-diffusion models.

Potential for improved option pricing methods.

Abstract

In mathematical finance a popular approach for pricing options under some Levy model is to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE) that usually does not allow an analytical solution while numerical solution brings some problems. In this paper we elaborate a new approach on how to transform the PIDE to some class of so-called pseudo-parabolic equations which are known in mathematics but are relatively new for mathematical finance. As an example we discuss several jump-diffusion models which Levy measure allows such a transformation.