美式選擇權之一般性靜態避險複製法

Abstract

本篇論文旨在利用Derman在1993年提出靜態避險投資組合複製法建構一個Heston (1993) 隨機波動度模型性下的美式選擇權評價模型，同時，我們以Fink (2003)在隨機波動度下建構靜態避險複製法評價障礙選擇權為架構，來評價美式選擇權，同時結合Chung and Shih(2009) 提出的美式選擇權靜態避險投資組合評價方法，將模型更一般化推廣至隨機波動度的環境下，以靜態避險複製投資組合的方式來評價美式選擇權的價值，並嘗試降低減少誤差以達成評價時的效率性。

This paper use static hedge portfolio of Derman et al.(1995) to construct an efficient method to evaluate American style option under Heston’s stochastic volatility model. We also refer to Fink (2003) static replication approach and static hedging and pricing American options provided by Chung and Shih (2009). This static hedge portfolio of American option is evaluated by applying the value-match and smooth-pasting conditions on the early exercise boundary. And try to use these schemes to reduce the error and show its efficiency.