利用靜態複製法與Repeated Richardson Extrapolation 評價CEV模型下的障礙選擇權

Abstract

本論文研製之目的為提供兼具效率與準確性的障礙選擇權評價方法，作者以Derman, Ergener, Kani (1995, DEK)發表的靜態複製法為基礎，並融合了兩種方法來評價障礙選擇權價格，希冀藉由此方法能夠迅速且有效的套用在CEV模型的架構中。本文嘗試以上限終止障礙買權(UOC)為例，透過DEK method我們可以簡單建構出投資組合來複製一個時間被均勻劃分的障礙選擇權，使其在觸及障礙時的價格歸零以達到基本複製，但為了能夠提升評價的準確性，作者額外使用了Chang, Chung, Stapleton (2007)文中使用的repeated Richardson extrapolation及Chung, Shih, Tsai (2010)所提出的theta-matching來作為改善的依據，最後也透過誤差估計的測試來鞏固模型的穩健性，並依其數值分析總結何種方法最能達到本文宗旨。

In this paper, the author attempts to modify the performance of hedging barrier options with static replication approach proposed by Derman, Ergener, and Kani(1995, DEK) and extrapolation method distributed by Chang, Chung, Stapleton (2007) under the constant elasticity of variance model of Cox and Ross (1976) in order to figure out whether the improved results show up. With the DEK method, the value of the portfolio can correspond the zero value of the barrier option at evenly cutting time points when the stock price hits the barrier, and then the author further adds the theta-matching condition in order to accurately approximate the results. Moreover, the author uses the repeated Richardson extrapolation, which allows us to discover the value of the approximation faster. Finally, by comparing these two methods, the author selects the most efficient one and test it with error estimation for the purpose of the accuracy.