彩虹阶梯栏杆选项

Q4 Business, Management and Accounting

Journal of Risk and Financial Management Pub Date : 2024-08-13 DOI:10.3390/jrfm17080356

Tristan Guillaume

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引用次数: 0

摘要

本文提供了各种彩虹阶梯障碍期权的精确分析公式。这些都是高度灵活和复杂的多资产障碍期权，其原理如下：期权的有效期被划分为几个时间段，在这些时间段内，不同的障碍会被监控到不同的标的资产。从数学角度来看，文章提供了多维几何布朗运动首次通过阶跃函数定义的边界时间的新结果。文章展示了如何以简单高效的方式实现所获得的期权估值公式。数值结果凸显了彩虹阶梯障碍期权对标的资产间相关性的强烈敏感性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Rainbow Step Barrier Options

This article provides exact analytical formulae for various kinds of rainbow step barrier options. These are highly flexible and sophisticated multi-asset barrier options based on the following principle: the option life is divided into several time intervals on which different barriers are monitored w.r.t. different underlying assets. From a mathematical point of view, new results are provided for the first passage time of a multidimensional geometric Brownian motion to a boundary defined as a step function. The article shows how to implement the obtained option valuation formulae in a simple and very efficient manner. Numerical results highlight a strong sensitivity of rainbow step barrier options to the correlations between the underlying assets.

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