台指選擇權Model-free隱含波動度之連動關係

Abstract

當選擇權價格在短期間內偏離買賣權等價理論(Put-Call Parity)時，表示出現選擇權隱含波動度價差不等於零的情形，短期間內買、賣權Model-free隱含波動度存在偏離的現象。利用單根檢定、向量自我迴歸模型、共整合檢定、向量誤差修正模型、因果關係檢定、衝擊反應分析及預測誤差變異數分解探討兩時間序列短期及長期之關聯性與互動關係。實證結果顯示買、賣權Model-free隱含波動度存在長期均衡的關係，且兩變數之資訊傳遞使兩者都受到對方的影響。透過衝擊反應分析及預測誤差變異數分解探討短期之互動關係，證實兩變數的雙向影響效果。整體而言，買、賣權Model-free隱含波動度之間的資訊是雙向傳遞的，雙向的資訊傳遞使兩者皆受到彼此的影響，出現偏離的情形後，皆在長期回到均衡狀態。

When option price deviates from Put-call Parity, option volatility spread will be non-zero. It means that call option Model-free implied volatility won’t be equal to put option Model-free implied volatility in a very short time. Investigate the interactive relationship between call and put option Model-free implied volatility through Unit Root Test, Vector Autoregression Model, Cointegration Test,Vector Error Correction Model,Granger Causality Test, Impulse Response Analysis and Forecast Error Variance Decomposition. The results show that there exists a long-run equilibrium relationship between two time series. In conclusion, two time series are affected by each others. The influences between two sides are bidirectional. Both call and put option Model-free implied volatility will back to long-run equilibrium after short-term deviation.