Forward evolution equations for knock-out options

Peter Carr, Ali Hirsa

Research output: Chapter in Book/Report/Conference proceedingChapter


We derive forward partial integrodifferential equations (PIDEs) for pricing up-and-out and down-and-out call options when the underlying is a jump diffusion. We assume that the jump part of the returns process is an additive process. This framework includes the Variance-Gamma, finite moment logstable, Merton jump diffusion, Kou jump diffusion, Dupire, CEV, arcsinh normal, displaced diffusion, and Black–Scholes models as special cases.

Original languageEnglish (US)
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Number of pages23
StatePublished - 2007

Publication series

NameApplied and Numerical Harmonic Analysis
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017


  • Forward equations
  • Jump diffusion
  • Knock-out options
  • L’evy processes
  • Partial integrodifferential equation (PIDE)

ASJC Scopus subject areas

  • Applied Mathematics


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