Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models

Andrey Itkin, Peter Carr

Research output: Contribution to journalArticle

Abstract

In mathematical finance a popular approach for pricing options under some Lévy model would be 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 a numerical solution also faces some problems. In this paper we develop a new approach on how to transform the PIDE into a class of so-called pseudo-parabolic equations which are well known in mathematical physics but are relatively new for mathematical finance. As an example we will discuss several jump-diffusion models which Lévy measure allows such a transformation.

Original languageEnglish (US)
Pages (from-to)63-104
Number of pages42
JournalComputational Economics
Volume40
Issue number1
DOIs
StatePublished - Jun 2012

Keywords

  • Finite-difference scheme
  • General stable tempered process
  • Jump-diffusion
  • Numerical method
  • Pseudo-parabolic equations
  • The Green function

ASJC Scopus subject areas

  • Economics, Econometrics and Finance (miscellaneous)
  • Computer Science Applications

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