کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1707778 | 1519470 | 2015 | 6 صفحه PDF | دانلود رایگان |
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.
Journal: Applied Mathematics Letters - Volume 43, May 2015, Pages 19–24