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

Fingerprint

Infinite Variance
Option Pricing
Nonparametric Bootstrap
Gamma Process
Correlated Data
Resampling
Point Process
Asymptotic Formula
Bootstrap
Paradigm
Valid
Option pricing

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Option pricing for infinite variance data. / Ishwaran, Hemant; Jahandideh, Mohammad T.; Zarepour, Mahmoud.

In: Statistics, Vol. 42, No. 3, 01.06.2008, p. 245-260.

Research output: Contribution to journalArticle

Ishwaran, H, Jahandideh, MT & Zarepour, M 2008, 'Option pricing for infinite variance data', Statistics, vol. 42, no. 3, pp. 245-260. https://doi.org/10.1080/02331880701830748
Ishwaran, Hemant ; Jahandideh, Mohammad T. ; Zarepour, Mahmoud. / Option pricing for infinite variance data. In: Statistics. 2008 ; Vol. 42, No. 3. pp. 245-260.
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