Option Pricing for Symmetric Lévy Returns with Applications

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

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Abstract

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
Volume22
Issue number1
DOIs
Publication statusPublished - Mar 2015

Keywords

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

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