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首页> 外文期刊>Journal of Economic Dynamics and Control >Pricing Parisian and Parasian options analytically
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Pricing Parisian and Parasian options analytically

机译：对巴黎期权和帕拉西亚期权进行定价分析

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摘要

In this paper, two analytic solutions for the valuation of European-style Parisian and Parasian options under the Black-Scholes framework are, respectively, presented. A key feature of our solution procedure is the reduction of a three-dimensional problem to a two-dimensional problem through a coordinate transform designed to combine the two time derivatives into one. Compared with some previous analytical solutions, which still require a numerical inversion of Laplace transform, our solutions, written in terms of double integral for the case of Parisian options but multiple integrals for the case of Parasian options, are both of explicit form; numerical evaluation of these integrals is straightforward. Numerical examples are also provided to demonstrate the correctness of our newly derived analytical solutions from the numerical point of view, through comparing the results obtained from our solutions and those obtained from adopting other standard finite difference approaches.
机译：本文分别提出了两种在Black-Scholes框架下对欧式巴黎期权和Parasian期权进行估值的解析方法。我们的求解过程的一个关键特征是通过将两个时间导数组合为一个的坐标变换将三维问题简化为二维问题。与一些以前的分析解决方案（仍需要对Laplace变换进行数值反演）相比，我们的解决方案都是显式形式，对于Parisian期权来说是双积分，对于Parasian期权来说是多重积分。这些积分的数值评估很简单。通过比较从我们的解决方案获得的结果和通过采用其他标准有限差分方法获得的结果，还提供了数值示例，以从数值的角度证明我们新导出的解析解的正确性。

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