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An Extension of the Chaos Expansion Approximation for the Pricing of Exotic Basket Options

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Author Info

  • Hideharu Funahashi

    ()
    (Mizuho Securities Co. Ltd. and Tokyo Metropolitan University)

  • Masaaki Kijima

    ()
    (Graduate School of Social Sciences, Tokyo Metropolitan University)

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    Abstract

    Funahashi and Kijima (2013) have proposed an approximation method based on the Wiener-Ito chaos expansion for the pricing of European-style contingent claims. In this paper, we extend the method to the multi-asset case with general local volatility structure for the pricing of exotic basket options such as Asian basket options. Through ample numerical experiments, we show that the accuracy of our approximation remains quite high even for a complex basket option with long maturity and high volatility.

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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP857.pdf
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    Bibliographic Info

    Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 857.

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    Date of creation: Apr 2013
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    Handle: RePEc:kyo:wpaper:857

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    Related research

    Keywords: Wiener-Ito chaos expansion; local volatility; average option; basket option; spread option; Asian basket option;

    This paper has been announced in the following NEP Reports:

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    1. Peter Ritchken & L. Sankarasubramanian & Anand M. Vijh, 1993. "The Valuation of Path Dependent Contracts on the Average," Management Science, INFORMS, vol. 39(10), pages 1202-1213, October.
    2. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
    3. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
    4. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
    5. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
    6. P. Pellizzari, 1998. "Efficient Monte Carlo Pricing of Basket Options," Finance 9801001, EconWPA.
    7. Jean-Pierre Fouque & Chuan-Hsiang Han, 2003. "Pricing Asian options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 353-362.
    8. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    10. Milevsky, Moshe Arye & Posner, Steven E., 1998. "Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 409-422, September.
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