Pricing Parisian down-and-in options

Song-Ping Zhu, Nhat-Tan Le, Wen-Ting Chen and Xiaoping Lu

Papers from arXiv.org

Abstract: In this paper, we price American-style Parisian down-and-in call options under the Black-Scholes framework. Usually, pricing an American-style option is much more difficult than pricing its European-style counterpart because of the appearance of the optimal exercise boundary in the former. Fortunately, the optimal exercise boundary associated with an American-style Parisian knock-in option only appears implicitly in its pricing partial differential equation (PDE) systems, instead of explicitly as in the case of an American-style Parisian knock-out option. We also recognize that the "moving window" technique developed for pricing European-style Parisian up-and-out options can be adopted to price American-style Parisian knock-in options as well. In particular, we obtain a simple analytical solution for American-style Parisian down-and-in call options and our new formula is written in terms of four double integrals, which can be easily computed numerically.

Date: 2015-11
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1511.01564

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