Edgeworth GARCH選擇權演算法的實證應用

本文分析股票的價格行為，並探討Edgeworth族選擇權演算法對台灣認購權證的評價與避險績效。研究發現股票報酬率顯著不服從常態分配，且具異質變異性，因此Black-Scholes模型明顯錯估權證價格。而Rubinstein(1998)所提出之Edgeworth二元樹法與Duanetal.(2003)所主張之Edgeworth GARCH選擇權演算法，納入標的股票報酬率的高階動差資訊，確能提升評價績效；其中EdgeworthGARCH演算法又優於Edgeworth二元樹法，尤其對於標的股票具有較低波動持續性的權證。同時，Edgeworth族演算法的運算速度頗有效率，當處理大量交易資料時，確有節省時間的優勢。唯EdgeworthGARCH演算法仍具顯著評價誤差，而標的股票日內波動性可以解釋此評價誤差。最後，避險績效測試結果顯示Black-Scholes模型優於Edgeworth族演算法。這可能是因為偏態係數的敏感變動降低權證delta值估計的準確性，因而導致較差的避險績效。

關鍵字

選擇權評價法； Edgeworth GARCH選擇權演算法；認購權證

並列摘要

The study applies the Edgeworth family option pricing algorithms to the pricing and hedging of stock warrants in Taiwan stock exchange. The results show that the distributions of underlying stock returns reject the assumption of Normal distribution, and the Black-Scholes model significantly underprices the sample warrants. On the other hand, with the information of high moments of underlying stock returns, the pricing performances of Edgeworth binomial option pricing algorithm (Rubinstein 1998) and Edgeworth GARCH option pricing algorithm (Duan et al. 2003) are superior to that of Black-Scholes model. Meanwhile, Edgeworth GARCH option pricing algorithm is better than the Edgeworth binomial option pricing algorithm, especially for the warrants with lower volatility persistence. Besides, Edgeworth family option pricing algorithms are more efficient in terms of computing time. However, the price differences of Edgeworth GARCH option pricing algorithm are still significant, and the intraday volatility of underlying stock can explain them. Finally, the hedging performance simulation shows GARCH family algorithms are disappointing. The reason behind their poor behavior may be the high variation of the daily estimate of the skewness parameter.