The Pricing of Multiple-Expiry Exotics
AbstractIn 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1302.3319.
Date of creation: Feb 2013
Date of revision: Aug 2013
Publication status: Published in Electronic Journal of Mathematical Analysis and Applications, Vol.1, No.2, July 2013, pp.247-259
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-03-02 (All new papers)
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- 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.
- Peter Buchen, 2004. "The pricing of dual-expiry exotics," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 101-108.
- Mark Broadie & Yusaku Yamamoto, 2003. "Application of the Fast Gauss Transform to Option Pricing," Management Science, INFORMS, vol. 49(8), pages 1071-1088, August.
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