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Analytical Approximation of Pricing Average Options under the Heston Model

Recent Advances in Financial Engineering, 2011

17 Pages Posted: 1 Nov 2011 Last revised: 14 Mar 2012

Akira Yamazaki

Hosei University - Graduate School of Business Administration

Date Written: November 16, 2011

Abstract

This paper proposes a new approximation formula for pricing average options under Heston’s stochastic volatility model. When using the formula based on the Gram-Charlier expansion, it is necessary to know any moments of an averaged underlying asset price. We try to derive an analytical solution of the moments under the Heston model. There are two key points of the derivation: One of them is to repeatedly apply change of a certain measure. Another is to sequentially solve a system of ordinary differential equations. Moreover, numerical examples support the accuracy of the proposed average option pricing formula.

Keywords: Heston model, average option, Gram-Charlier expansion, moment, Girsanov transform

Suggested Citation

Yamazaki, Akira, Analytical Approximation of Pricing Average Options under the Heston Model (November 16, 2011). Recent Advances in Financial Engineering, 2011. Available at SSRN: https://ssrn.com/abstract=1920159

Akira Yamazaki (Contact Author)

Hosei University - Graduate School of Business Administration ( email )

Japan

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