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Stochastic Expansion for the Pricing of Asian and Basket Options

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  • Fabien Le Floc'h

Abstract

We present closed analytical approximations for the pricing of basket options, also applicable to Asian options with discrete averaging under the Black-Scholes model with time-dependent parameters. The formulae are obtained by using a stochastic Taylor expansion around a log-normal proxy model and are found to be highly accurate for Asian options in practice as well as for vanilla options with discrete dividends.

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  • Fabien Le Floc'h, 2024. "Stochastic Expansion for the Pricing of Asian and Basket Options," Papers 2402.17684, arXiv.org, revised Aug 2024.
    • Handle: RePEc:arx:papers:2402.17684
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    References listed on IDEAS

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    1. M. H. Vellekoop & J. W. Nieuwenhuis, 2006. "Efficient Pricing of Derivatives on Assets with Discrete Dividends," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 265-284.
    2. Jherek Healy, 2021. "The Pricing of Vanilla Options with Cash Dividends as a Classic Vanilla Basket Option Problem," Papers 2106.12971, arXiv.org.
    3. Pierre Étor� & Emmanuel Gobet, 2012. "Stochastic Expansion for the Pricing of Call Options with Discrete Dividends," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(3), pages 233-264, August.
    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. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
    6. 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.
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