Download This Paper Open PDF in Browser

Pricing Average Options Under Time-Changed Levy Processes

31 Pages Posted: 6 Apr 2011 Last revised: 17 Mar 2014

Akira Yamazaki

Hosei University - Graduate School of Business Administration

Date Written: July 19, 2011

Abstract

This paper presents an approximate formula for pricing average options when the underlying asset price is driven by time-changed Levy processes. Time-changed Levy processes are attractive to use for a driving factor of underlying prices because the processes provide a flexible framework for generating jumps, capturing stochastic volatility as the random time change, and introducing the leverage effect. There have been very few studies dealing with pricing problems of exotic derivatives on time-changed Levy processes in contrast to standard European derivatives. Our pricing formula is based on the Gram-Charlier expansion and the key of the formula is to find analytic treatments for computing the moments of the normalized average asset price. In numerical examples, we demonstrate that our formula give accurate values of average call options when adopting Heston's stochastic volatility model, VG-CIR, and NIG-CIR models.

Keywords: average options, time-changed Levy processes, Gram-Charlier expansion, affine processes, quadratic Gaussian processes

JEL Classification: G13, C63

Suggested Citation

Yamazaki, Akira, Pricing Average Options Under Time-Changed Levy Processes (July 19, 2011). Review of Derivatives Research, Vol. 17, No. 1, 2014. Available at SSRN: https://ssrn.com/abstract=1803089 or http://dx.doi.org/10.2139/ssrn.1803089

Akira Yamazaki (Contact Author)

Hosei University - Graduate School of Business Administration ( email )

Japan

Paper statistics

Downloads
204
rank
130,411
Abstract Views
1,050
PlumX