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Pricing Parisian down-and-in options

Journal Article


Abstract


  • All rights reserved. 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.

Publication Date


  • 2015

Citation


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

Scopus Eid


  • 2-s2.0-84918556525

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4511

Has Global Citation Frequency


Number Of Pages


  • 5

Start Page


  • 19

End Page


  • 24

Volume


  • 43

Issue


  • May

Place Of Publication


  • United Kingdom

Abstract


  • All rights reserved. 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.

Publication Date


  • 2015

Citation


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

Scopus Eid


  • 2-s2.0-84918556525

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4511

Has Global Citation Frequency


Number Of Pages


  • 5

Start Page


  • 19

End Page


  • 24

Volume


  • 43

Issue


  • May

Place Of Publication


  • United Kingdom