隨機波動度下以近似履約曲面訂價美式選擇權

Pricing American Options under Stochastic Volatility Using Approximate Exercise Surface

陳映亘(Ying-Shiuan Chen)

指導教授 ： 呂育道

國立臺灣大學/管理學院/財務金融學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201901718

摘要

Heston 的隨機波動度模型不僅放寬了 Black-Scholes 的固定波動度假設，使得其可以更貼近實證資料，如報酬厚尾分佈(fat return tail)、波動的群聚現象(volatility clustering)等，另外也有著方便計算的歐式選擇權封閉解。但在美式選擇權的情況便複雜許多，因為其牽涉到履約曲面的計算，本篇論文延伸 Chiarella and Ziogas (2005) 之訂價方法，採用近似履約曲面並結合數值積分方式訂價選擇權，可以在十分有效率的情況下計算選擇權價格，快速幫助判斷是否需要履約。

關鍵字

隨機波動度 ； 美式選擇權 ； 近似履約曲面

並列摘要

Heston's model not only relaxes Black-Scholes's fixed volatility assumptions, but also reflects empirical situations, such as fat return tails, volatility clustering, etc. Moreover, Heston's models provides closed solution to European option that is easy to calculate. However, calculating American options is much more complicated since it involves calculating the exercise surface. This research extends the pricing method of Chiarella and Ziogas (2005) by approximating exercise surfaces with numerical integration, which significantly improves pricing efficiency.

並列關鍵字

Heston’s model ； American options ； approximate exercise surface

參考文獻

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