Hedging error as generalized timing risk
Hedging error as generalized timing risk
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DOI：
10.1080/14697688.2022.2154255
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发表时间：
2023-01
影响因子：
1.3
通讯作者：
J. Akahori;F. Barsotti;Y. Imamura
中科院分区：
文献类型：
--
作者：
J. Akahori;F. Barsotti;Y. Imamura
本文介绍了一种方法来解决与外汇衍生品套期相关的套期误差，其付款时间在开始时是未知的。我们推导了一维设置的数学表示：我们识别和描述了套期误差，并讨论了套期误差作为广义时机风险的经济直觉。然后，我们提供了它的数学积分表示：(i)将套期保值错误分解为障碍期权中的特定位置集，（ii）将该过程重复到二阶以减少套期保值错误成本。我们通过一个专门的数值研究提供了一个说明性的例子。从理论的角度来看，本文阐述了未来扩展的基础：(i)建立一个一般的多维框架，（ii）在更高的阶上重新迭代过程，（iii）用先进的分析方法和技术研究桥梁。
This paper introduces a methodology to disentangle the hedging error associated with the hedging of exotic derivatives, whose payment time is unknown at inception. We derive the mathematical representation for a one-dimensional setting: we identify and characterize the hedging error and discuss the economic intuition of hedging error as a generalized timing risk. We then provide its mathematical integral representation to: (i) disentangle the hedging error into a specific set of positions in barrier options, (ii) re-iterate the procedure to the second order to reduce the hedging error cost. We provide an illustrative example via a dedicated numerical study. From a theoretical point of view, this paper states the foundations for future extensions in the directions of: (i) building a general multidimensional framework, (ii) re-iterating the procedure to higher orders, (iii) investigate the bridge with advanced analytics methodologies and techniques.