利維過程效率方法在台灣選擇權市場之應用

Efficient Fourier Methods for Lévy Processes: Applications in Option Pricing in Taiwan

方民(Ming Fang)

指導教授 ： 王銘杰

國立暨南國際大學/管理學院/國際企業學系/博士(2016年)

摘要

本文使用不連續的跳躍模型，來探討對於台灣選擇權市場的定價能力，本文使用風險中立機率測度來評價選擇權，在最小平方誤校正之下，運用快速分數傅立葉轉換方式計算出選擇權定價，VG模型有最佳的的模型預測誤差，表示使用Lévy能改善選擇權模型的定價能力。在確定VG模型具有良好解釋能力後，本文針對選擇權市場價格進行模型校估，選取發行開始日到2012年共15萬筆的選擇權合約，同樣亦得到VG模型確實具有良好的預測選擇權定價能力。本文接著繼續探討選擇權定價計算之隱含波動性與衍生性金融商品期貨之關聯性，發現選擇權隱含波動性對期貨價格波動有顯著影響力，且呈現負相關。本論文針對金融風暴期間2007-2009年特別進行分析，對於投資人進行避險具有極大參考價值。
確定選擇權隱含波動性對期貨價格有負向影響後，本文探討交易策略的避險效果，使用買進買權以及賣出期貨之策略，結果指出無論是採用任何一種價性包含深價內選擇權、價平選擇權以及深價外選擇權，採用VG模型之避險效果均優於BS模型。

關鍵字

利微過程 ； 快速分數傅立葉轉換 ； 選擇權定價 ； 避險效果

並列摘要

This paper presents an efficient option pricing method for calibrating exponential Lévy models to a finite set of observed option prices. To examine the option pricing efficiency under exponential Lévy models, we compare the pricing errors and predictive power of exponential Lévy models with the Black-Scholes model. We also examine the 2007-2009 financial crisis period which the investors consider as a worth-meaning issue.
We adapt the global minimization algorithms to calibrate the parameter based on the characteristic function and the Fractional Fast Fourier Transform. We find the option pricing efficiency of VG outperform than other models. Second, we adapt all the options with the whole moneyness and find out with the implied approach, the VG outperform the BS. Third, the options implied volatilities derived on the BS and the VG are included to construct the spot-futures hedging portfolios and compare the hedging efficiency. The results suggest that the investors make their portfolios shall take options and futures into account since the options implied volatilities can improve the hedging efficiency. Finally, we investigate the dynamic hedging performance using the BS or VG models. Consider the dynamic hedging of a call option using a single-instrument hedge, the futures contract written on the underlying index. We find out the VG model provide good hedging performance over BS over all moneyness groups.

並列關鍵字

Lévy process FRFT ； Options Pricing ； Hedging

參考文獻

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