Time-changed Lévy processes and option pricing

Peter Carr, Liuren Wu

Research output: Contribution to journalArticle

Abstract

The classic Black-Scholes option pricing model assumes that returns follow Brownian motion, but return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non-normal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. Time-changed Lévy processes can simultaneously address these three issues. We show that our framework encompasses almost all of the models proposed in the option pricing literature, and it is straightforward to select and test a particular option pricing model through the use of characteristic function technology.

Original languageEnglish (US)
Pages (from-to)113-141
Number of pages29
JournalJournal of Financial Economics
Volume71
Issue number1
DOIs
StatePublished - Jan 2004

Keywords

  • Fourier transforms
  • Lévy processes
  • Measure change
  • Option pricing
  • Random time change

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Economics and Econometrics
  • Strategy and Management

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