Forward evolution equations for knock-out options

Peter Carr, Ali Hirsa

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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
Pages195-217
Number of pages23
Edition9780817645441
DOIs
StatePublished - 2007

Publication series

NameApplied and Numerical Harmonic Analysis
Number9780817645441
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

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  • Cite this

    Carr, P., & Hirsa, A. (2007). Forward evolution equations for knock-out options. In Applied and Numerical Harmonic Analysis (9780817645441 ed., pp. 195-217). (Applied and Numerical Harmonic Analysis; No. 9780817645441). Springer International Publishing. https://doi.org/10.1007/978-0-8176-4545-8_11