資產價格條件下的隨機波動美式選擇權靜態避險

Abstract

本篇論中，我們延續 Derman, Ergener, and Kani (1995) and Chung, Shih, and Tsai (2009) 的靜態避險方法，將之用於隨機波動的美式賣選擇權上，Chung,Shih,and Tsai (2009)，利用 Black-Scholes 模型，並使用 valuing matching 和 兩種邊界條 件去建構一個美式選擇權的靜態避險。而我們的模型相比於 Chung, Shih, and Tsai 有兩個不同之處。首先，基於隨機波動的假設，我們用 Heston 模型 而不是用 Black-Scholes 模型。其二，我們將每個時間切點上最有可能的波動度，加入在要 匹配的邊界條件中。根據實驗結果顯示，我們的模型在隨機波動的美式賣權中有 良好的避險效果，同時，我們也特別針對賠錢賠比較多，或賺錢賺比較多的避險 路徑做分析。

In this thesis, we extend static hedge methods proposed in Derman, Ergener, and Kani (1995) and Chung, Shih, and Tsai (2009) to evaluate American options under the stochastic volatility model conditional on asset price. Based on Chung, Shih, and Tsai (2009), the static hedge method of American options is formulated by applying the valuing matching and smooth-pasting conditions. However, our approach has two main differences from Chung, Shih, and Tsai’s (2009) model. First, we use the Heston stochastic-volatility option pricing model instead of the Black-Scholes model. Second, we apply the most likely volatility, which is conditional on asset price, on the early exercise boundary when determining the weight and strike price of the options in the static-hedge option portfolio. The result shows that the proposed model performs well on hedge performance for American put options under stochastic volatility. The scenarios for extreme gains and losses are also analyzed.