The forward PDE for european options on stocks with fixed fractional jumps

Peter Carr, Alireza Javaheri

Research output: Contribution to journalArticle

Abstract

We derive a partial integro differential equation (PIDE) which relates the price of a calendar spread to the prices of butterfly spreads and the functions describing the evolution of the process. These evolution functions are the forward local variance rate and a new concept called the forward local default arrival rate. We then specialize to the case where the only jump which can occur reduces the underlying stock price by a fixed fraction of its pre-jump value. This is a standard assumption when valuing an option written on a stock which can default. We discuss novel strategies for calibrating to a term and strike structure of European options prices. In particular using a few calendar dates, we derive closed form expressions for both the local variance and the local default arrival rate.

Original languageEnglish (US)
Pages (from-to)239-253
Number of pages15
JournalInternational Journal of Theoretical and Applied Finance
Volume8
Issue number2
DOIs
StatePublished - Mar 2005

Keywords

  • Credit risk
  • Default risk
  • Forward equations
  • Jump diffusion

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

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