重設選擇權之評價與避險操作

Reset Options Pricing and Hedging

林岳賢(Yue-Xian Lin) ； 李存修(Tsun-Siou Lee)

《中國財務學刊》 7卷2期 (1999/08) Pp. 113-150

https://doi.org/10.6545/JoFS.1999.7(2).5

摘要

重設選擇權是一種允許履約價格改變的選擇權。它可視為眾多障礙選擇權（barrier options）中的一個特例，我們有許多方法來評價它。本文提出一個動態拆解股價樹（Dynamic Decomposition Algorithm, DDA）的評價方法，不僅有滿意的收斂速度，而且非常一般化：可以用來評價具有n個重設期間、每個重設期間內含有mi個重設價格、各個重設期間彼此的關係可為獨立或相依的重設型權證，而且不管是連續觀察（continuous monitoring）或間斷觀察（discrete monitoring），均可適用。除了價格的決定以外，本文也探討重設型權證在避險時所特有的Delta跳躍與負Delta值等問題的成因與解決之道。透過模擬，我們評估了各種不同的避險操作方法下的避險績效。最後我們透過比較靜態分析（comparative analysis）探討重設型權證各個子選擇權的價格行為，其結果不但幫助我們更深入地瞭解評價方法背後的邏輯，也對實務上研發新產品或修改既有產品有所幫助。

關鍵字

重設選擇權 ； 動態拆解法 ； Delta跳躍 ； 負Delta值

並列摘要

A reset option is an option whose strike price will be changed in a pre -specified manner when certain conditions are met within a certain period of time. When the condition is defined on the price of the underlying asset hilling certain level, the reset option is essentially a special case of barrier options. Pricing techniques up to now rely on either numerical analysis or simulation. We develop a new pricing technique called Dynamic Decomposition Algorithm (DDA), which is general enough to cover the cases of n reset periods, each having m, reset prices. The proposed DDA works well under discrete monitoring as well as continuous monitoring without sacrificing the speed of convergence. The problems of delta jumps and negative deltas may arise in hedging reset options, especially when the price of the underlying asset is close enough to the reset triggering point and the option is close to expiration. We design alternative hedging schemes and compare their hedging performances through simulations. Finally, comparative static analysis is provided with respect to the changes in premiums of reset options in response to changes in all relative parameters.

並列關鍵字

Reset Option ； Dynamic Decomposition Algorithm ； Delta jump ； Negative Delta