Pricing Parisian down-and-in options

Authors

Song-Ping Zhu, University of WollongongFollow
Nhat Tan Le, University of WollongongFollow
Wenting Chen, University of WollongongFollow
Xiaoping Lu, University of WollongongFollow

RIS ID

97000

Publication Details

Zhu, S., Le, N., Chen, W. & Lu, X. (2015). Pricing Parisian down-and-in options. Applied Mathematics Letters, 43 (May), 19-24.

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 by Zhu and Chen (2013) for pricing European-style Parisian up-and-out call 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.