在隨機波動度模型下，以建構避險投資組合與二項樹模型的方式定價美式選擇權

Abstract

本論文延伸了Chung and Shih (2009) 的研究成果至Heston (1993) 隨機波動模型，我們先以Nelson and Ramaswamy (1990) 的方式建構波動度二項樹，並在每個節點上建立歐式賣權，以價值匹配與平滑貼合條件決定每個歐式賣權的權重，我們稱為動-靜態避險投資組合。此定價結果與Beliaeva and Nawalkha (2010) 吻合，並在不同參數下的定價表現皆十分出色，最後以Chung, Huang, Shih, and Wang (2019) 提供的方式評價避險投資組合的表現，結果顯示動-靜態避險組合有良好的避險表現。

This study extends the work of Chung and Shih (2009) to the Heston (1993) stochastic volatility model. We first construct a volatility binomial tree following the method proposed by Nelson and Ramaswamy (1990), and then construct European put options at each node. The weights of these European options are determined using the value-matching and smooth-pasting conditions. We refer to this as a dynamic-static hedging portfolio. The pricing results are consistent with those of Beliaeva and Nawalkha (2010), and the model performs well under various parameter settings. Finally, we evaluate the performance of the hedging portfolio using the approach proposed by Chung, Huang, Shih, and Wang (2019), and the results demonstrate that the dynamic-static hedging strategy exhibits strong hedging effectiveness.