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The Pricing of Multiple-Expiry Exotics

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  • Hyong-Chol O
  • Mun-Chol KiM

Abstract

In this paper we extend Buchen's method to develop a new technique for pricing of some exotic options with several expiry dates(more than 3 expiry dates) using a concept of higher order binary option. At first we introduce the concept of higher order binary option and then provide the pricing formulae of $n$-th order binaries using PDE method. After that, we apply them to pricing of some multiple-expiry exotic options such as Bermudan option, multi time extendable option, multi shout option and etc. Here, when calculating the price of concrete multiple-expiry exotic options, we do not try to get the formal solution to corresponding initial-boundary problem of the Black-Scholes equation, but explain how to express the expiry payoffs of the exotic options as a combination of the payoffs of some class of higher order binary options. Once the expiry payoffs are expressed as a linear combination of the payoffs of some class of higher order binary options, in order to avoid arbitrage, the exotic option prices are obtained by static replication with respect to this family of higher order binaries.

Suggested Citation

  • Hyong-Chol O & Mun-Chol KiM, 2013. "The Pricing of Multiple-Expiry Exotics," Papers 1302.3319, arXiv.org, revised Aug 2013.
    • Handle: RePEc:arx:papers:1302.3319
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    References listed on IDEAS

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    1. Peter Buchen, 2004. "The pricing of dual-expiry exotics," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 101-108.
    2. Lishang Jiang, 2005. "Mathematical Modeling and Methods of Option Pricing," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 5855, February.
    3. Mark Broadie & Yusaku Yamamoto, 2003. "Application of the Fast Gauss Transform to Option Pricing," Management Science, INFORMS, vol. 49(8), pages 1071-1088, August.
    4. Longstaff, Francis A, 1990. "Pricing Options with Extendible Maturities: Analysis and Applications," Journal of Finance, American Finance Association, vol. 45(3), pages 935-957, July.
    5. Ingersoll, Jonathan E, Jr, 2000. "Digital Contracts: Simple Tools for Pricing Complex Derivatives," The Journal of Business, University of Chicago Press, vol. 73(1), pages 67-88, January.
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