Analytical Approximation of Pricing Average Options under the Heston Model

Akira Yamazaki
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Akira Yamazaki: Graduate School of Economics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Mizuho-DL Financial Technology Co., Ltd., 1-3, Otemachi 1-chome, Chiyoda-ku, Tokyo 100-0004, Japan

Chapter 10 in Recent Advances in Financial Engineering 2011, 2012, pp 203-220 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractThis 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: Financial Engineering; Mathematical Finance; Money & Banking; Risk Management; Real Option; Corporate Finance; Computational Finance (search for similar items in EconPapers)
Date: 2012
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