Option Pricing for Symmetric Lévy Returns with Applications

Kais Hamza, Fima C. Klebaner, Zinoviy Landsman, Ying Oon Tan

Research output: Contribution to journalArticlepeer-review


This paper considers options pricing when the assumption of normality is replaced with that of the symmetry of the underlying distribution. Such a market affords many equivalent martingale measures (EMM). However we argue (as in the discrete-time setting of Klebaner and Landsman in Methodology and Computing in Applied Probability, 2007, doi:10.1007/s11009-007-9038-2) that an EMM that keeps distributions within the same family is a “natural” choice. We obtain Black–Scholes type option pricing formulae for symmetric Variance-Gamma and symmetric Normal Inverse Gaussian models.

Original languageEnglish
Pages (from-to)27-52
Number of pages26
JournalAsia-Pacific Financial Markets
Issue number1
StatePublished - Mar 2014

Bibliographical note

Publisher Copyright:
© 2014, Springer Japan.


  • Equivalent martingale measure
  • Lévy processes
  • Normal Inverse Gaussian process
  • Option pricing
  • Risk-neutral pricing
  • Symmetric distribution
  • Variance Gamma process

ASJC Scopus subject areas

  • Finance


Dive into the research topics of 'Option Pricing for Symmetric Lévy Returns with Applications'. Together they form a unique fingerprint.

Cite this