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Pricing Parisian down-and-in options

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

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.

Suggested Citation

  • Song-Ping Zhu & Nhat-Tan Le & Wen-Ting Chen & Xiaoping Lu, 2015. "Pricing Parisian down-and-in options," Papers 1511.01564, arXiv.org.
    • Handle: RePEc:arx:papers:1511.01564
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    References listed on IDEAS

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