路徑相依衍生性商品的避險

Hedging Strategies against Path-Dependent Contingent Claims

黃士峰(Shih-Feng Huang) ； 黃景榆(Ching-Yu Huang)

《中國統計學報》 47卷3期 (2009/09) Pp. 194-218

https://doi.org/10.29973/JCSA.200909.0004

摘要

在金融市場中，對路徑相依的衍生性金融商品建立避險策略不僅重要且具有挑戰性。文獻上常以靜態避險或動態避險處理此避險問題，但靜態避險不易規避大部分的期末風險，而動態避險雖可透過連續交易與變動其避險部位以降低期末風險，但也因此需要付出較多的交易成本。爲了在降低期末風險與減少交易成本之間取得平衡，本文提出一種新的避險策略，此避險策略除了在期初時建立避險投資組合外，只需要在該衍生性商品的存續期間中選擇一適當的時閒點調整避險部位，此一避險策略不僅能有效地降低動態避險策略在避險過程中所必須付出的避險成本，亦能同時具有良好的避險功能。文中我們特別針對當標的資產滿足幾何布朗運動時，以單一標的資產的障礙選擇權與雙重標的資產且標的資產間具有相前性的喜馬拉雅選擇權爲例，說明此一避險策略的操作過程，並雄導出其避險部位的理論解。模擬研究亦證實本文所提出的避險策略，對於障礙選擇權和喜馬拉雅選擇權具有良好的避險成果。

關鍵字

障礙選擇權 ； 第一次碰觸時間 ； 避險 ； 喜馬拉雅選擇權 ； 多資產衍生性商品 ； 路徑相依衍生性商品

並列摘要

The construction of hedging strategies against path-dependent contingent claims is one of the most important financial challenges. In the literature, many static and dynamic hedgings are proposed to solve this hedging problem. Since dynamic hedging comprises more relocation opportunities than static one, it is usually superior to static hedging in terms of risk reduction. However, the increasing frequency of portfolio rebalancing costs more transaction fees. Due to the trade-off between risk reduction and transaction costs, we propose a new hedging strategy which rebalances the hedging positions only once during the duration of the contingent claim. We illustrate the proposed hedging strategy for single-asset barrier options and multi-asset Himalaya options when the underlying assets follow the geometric Brownian motion processes. The hedging positions of the portfolio are derived and simulation studies show that the proposed strategy provides good hedging performance for barrier and Himalaya options.

並列關鍵字

Barrier option ； first passage time ； hedging ； Himalaya option ； multi-asset derivatives ； path-dependent derivatives

參考文獻

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