隨機波動度下美式上出局賣權之一般靜態避險法

Abstract

本篇論文以Derman, Ergener, and Kani (1995) 提出的靜態避險投資組合複製法為基礎，結合Chung, Shih, and Tsai (2013) 的研究方法，建構出美式上出局賣權於隨機波動度下的評價模型。同時，我們也以Fink (2003) 於隨機波動度下建構靜態避險法評價障礙選擇權的方法為架構，延伸此方法於美式上出局賣權的障礙價格及提前履約邊界上，結合運用等價法及平滑法來處理其邊界問題。 同時，我們也提供一個調整後的外部有限差分法，作為提供美式上出局賣權價格的參考依據。 本篇的數值方法指出，運用 Fink (2003)架構下建構出的一般化靜態複製法所求出的投資組合價值約莫低估3%，而Fink (2003)所提出用以媒合不同波動度狀態的方法，對於提升投資組合價值精確度的效果是有限的。

This thesis extends the static hedging portfolio (SHP) methods of Derman, Ergener, and Kani (1995) and Chung, Shih, and Tsai (2013) to evaluate American up-and-out put options under the stochastic volatility model. Based on Fink’s (2003) framework, we construct an SHP to match the knock-out boundary, barrier, and the early exercise boundary conditions of American up-and-out put options according to the value-matching and smooth-pasting conditions. Moreover, a modified explicit finite difference method is also developed to compute the comparison benchmark.Our numerical results indicate that the generalized static replication method underestimate the value of AUOP options about 3% and Fink’s (2003) multi-state for volatility has limited ability to improve the pricing accuracy.