一個新的領先指標應用於台指選擇權隱含波動性預測的行為分析

Abstract

一般認為選擇權的時間價值會隨著時間的流逝以及被履約的可能性減少而呈現出遞減的現象，而且距離到期日越接近則有加速遞減的情形，直到到期日當天將遞減為零。然而，事實上時間價值並不必然隨著時間的流逝而降低，反倒可能因為行情變化而上揚；並且在到期日之前，價內數檔的選擇權就有可能出現負值的時間價值，這不只製造出可能的套利空間，也違反了一般認知的基本公設，更顯示出投資人對於標的物後市行情的看法不再是遵循對數常態分配，而是有明確的上漲或下跌方向性。本研究的目的在於針對選擇權時間價值真實意義的重新檢視，以及瞭解選擇權時間價值的變化是否與現貨價格的漲跌存在相關性。

本研究所提出的正向期望值模型可克服目前在使用隱含波動率時所面臨的假設錯誤及計算繁複，配合適當的臨界值可以得到良好的波動預測結果。

It is said that the time value of options will decay within the time passing and the chance of to be exercised decreasing. Also it goes faster when coming closer to the expiration date until it becomes zero . But the time value is not actually decay within the time passing － oppositely, it may follow the underlying raising. Some time value of in-the-money options might be negative, and it may cause some chance to arbitrage. Also it shows that people who forecast the underlying get the bullish or bearish tendency instead of following the log-normal distribution. This study focus on discovering the real purport of time value of options, and understanding the relationship between the time value of options and the change of underlying price.

The Positive Expectation model, which is proposed, is able to overcome some weakness of Implied Volatility model. With Suitable threshold, it can produce good forecasting accuracy.