Option Pricing for Symmetric Lévy Returns with Applications

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

doi:10.1007/s10690-014-9192-9

Option Pricing for Symmetric Lévy Returns with Applications

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

Department of Statistics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	27-52
Number of pages	26
Journal	Asia-Pacific Financial Markets
Volume	22
Issue number	1
DOIs	https://doi.org/10.1007/s10690-014-9192-9
State	Published - Mar 2014

Bibliographical note

Publisher Copyright:
© 2014, Springer Japan.

Keywords

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

ASJC Scopus subject areas

Finance

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10.1007/s10690-014-9192-9

Cite this

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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.",

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KW - Lévy processes

KW - Normal Inverse Gaussian process

KW - Option pricing

KW - Risk-neutral pricing

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Option Pricing for Symmetric Lévy Returns with Applications

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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