台指選擇權隱含波動率之探討

本文使用台灣指數選擇權的價格資料，來觀察選擇權隱含波動率的型態，並探討在美國次級房貸和歐洲債券等金融危機期間，波動率的型態是否會有所改變。其次，討論是否有適當的波動性模型，能描述隱含波動率的型態，並具有良好的模型配適度。最後，探討隱含波動率對實際波動率的預測能力，以及選擇權交易在金融危機期間所提供的早期預警功能。實證結果指出隱含波動率在樣本期間並未具有微笑曲線型態，然而以歐債危機的型態最為接近，同時在金融危機和市場穩定期間，波動率型態未有明顯差異。若使用數種波動性函數來描述其型態，以標準化價性指標並納入價平隱含波動率的模型表現最佳，但未有模型能夠完整解釋隱含波動率之變化。此外，次級房貸期間的台指選擇權具有預警訊號，可預測未來的極端波動，顯示此期間的市場交易相當有效率，對投資人提供有用的訊息。

關鍵字

隱含波動率；波動率微笑曲線；隱含波動率模型

並列摘要

This study estimates the implied volatilities of Taiwan stock index options and tests for the presence of a smile pattern, or U-shape, pattern across the moneyness levels of those options. The analysis also considers whether the smile patterns differ between stable financial markets and those that are in crisis. Using multiple implied volatility functions, this study examines which model captures the smile pattern and offers the best goodness of fit with the model specifications. With this evidence, the authors determine whether implied volatility can predict future volatility. The empirical results do not reveal a smile pattern in implied volatilities; however, the shape becomes more evident during the European sovereign debt crisis, relative to the U.S. subprime mortgage financial crisis. Nor do the patterns vary according to financial market conditions. The implied volatility functions can improve option valuation, and the best performance results from a quadratic function of the options’ standardized moneyness with the level of implied at-the-money volatility. However, no single model performs well for options across all moneyness levels. Finally, the implied volatility includes other volatility indicators that can predict future market volatility, and provide an early warning signal of extreme volatility, as was experienced during the U.S. subprime mortgage financial crisis.