隨機過程能否解釋隱含波動率的形態？以台灣衍生性

Does The Stochastic Process Explain The Bizarreness of Implied Volatility Function? Evidences from Taiwan Derivative Markets

隱含波動率微笑現象始終為選擇權理論探討話題，部份學說相信此是因罕見事件其實比想像中還常見的報酬率胖尾分配所造成，另說則相信此是因選擇權所連結資產報酬率的變異數異質性所造成。本研究以台灣指數與個股選擇權市場為對象，實證結果認為經濟性因素，如選擇權合約供需數量與淨買壓，才是形成隱含波動率形態的主要原因。實證結果亦顯示，報酬率分配與隱含波動率形態無顯著關係；造市者因應市場需求以進行避險的限制套利假說獲得支持；模擬分析中產生的超常報酬，會隨選擇權合約價格深度不同而不同，與隱含波動率並非水平直線情況吻合。

The mysterious smile shown on implied volatility (IV) function of options has lastingly been discussed. A major stream of studies attributes the smile is reproduced by the transformed return distributions due to higher chance of rare events; some literature attribute the smile is caused by the dynamic variance of underlying asset. However, this study, based a Taiwan case of index and individual stock options market, advocated a more economic reason related with a strength of supply and demand, the net buying pressure (NBP), which is the main factor to affect the shape of IV function especial for index options. The analysis revealed that, the return distribution of underlying asset is not necessarily related with IV; the market maker hedges itself referring to demand of contracts thus the limits to arbitrage hypothesis is supported; the abnormal return generated from simulations supported that price premium shall be collected by different series of contracts and a non- horizontal IV as well.