Option pricing for infinite variance data

Hemant Ishwaran, Mohammad T. Jahandideh, Mahmoud Zarepour

Research output: Contribution to journalArticle

Abstract

We consider the asymptotic option pricing formula under an infinite variance paradigm using a randomized version of the Cox-Ross-Rubinstein binomial option pricing approach. We discuss practical difficulties in applying the asymptotic formula and suggest a non-parametric bootstrap as an estimation technique. Using point process theory, the asymptotic consistency of the bootstrap approach is established under a resampling scheme of m=o(n). We briefly discuss extensions to correlated data and show the option pricing formula may no longer be valid in such settings. Finally, we consider a finite variance setting involving innovations from a variance gamma process. We derive the asymptotic option pricing formula and show that the non-parametric bootstrap is consistent.

Original languageEnglish
Pages (from-to)245-260
Number of pages16
JournalStatistics
Volume42
Issue number3
DOIs
StatePublished - Jun 1 2008
Externally publishedYes

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Keywords

  • Infinite variance
  • Moving averages
  • Nonparametric bootstrap
  • Option pricing
  • Point processes
  • Stable laws

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

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