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Analytical Approximation of Pricing Average Options under the Heston Model

In: Recent Advances In Financial Engineering 2011

Author

Listed:
  • 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)

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.

Suggested Citation

  • Akira Yamazaki, 2012. "Analytical Approximation of Pricing Average Options under the Heston Model," World Scientific Book Chapters, in: Akihiko Takahashi & Yukio Muromachi & Hidetaka Nakaoka (ed.), Recent Advances In Financial Engineering 2011, chapter 10, pages 203-220, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814407335_0010
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