BARRIER OPTIONS PRICING WITH JOINT DISTRIBUTION OF GAUSSIAN PROCESS AND ITS MAXIMUM

Pingjin Deng () and Xiufang Li ()
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Pingjin Deng: School of Finance, Nankai University, Tianjin 300350, P. R. China
Xiufang Li: School of Finance, Nankai University, Tianjin 300350, P. R. China

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 06, 1-18

Abstract: Barrier options are one of the most popular exotic options. In this contribution, we propose a performance barrier option, which is a type of barrier option defined with the Nth period logarithm return rate process on an underlying asset over the time interval [0,T], N ≤ T ≤ 2N. We show that the price of this performance barrier option is determined by the joint distribution of a Slepian process and its maximum. Furthermore, we derive a tractable formula for this joint distribution and obtain explicit formulas for the up-out-call performance option and up-out-put performance option.

Keywords: Barrier option; up-out-call performance option; up-out-put performance option; options pricing; Slepian process; boundary noncrossing probability (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S021902491750042X

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