動態隱含波動度模型：以台指選擇權為例

Dynamic Implied Volatility Functions in Taiwan Options Market

本文提出一動態隱含波動度函數模型，以改善一般隱含波動度函數缺乏時間序列訊息且無法動態配適資料的缺點。本文以統計檢定方法及交易策略之獲利能力檢定模型的預測能力是否具有統計及經濟上的顯著性。以台指選擇權之隱含波動度為標的，和幾個常用的波動度模型比較後的實證結果發現，本文提出的隱含波動度函數模型具備較佳的樣本內資料配適能力；對於樣本外隱含波動度及選擇權價格的預測能力亦優於其他波動度函數模型。關於經濟上的顯著性，在不考慮交易成本下，本文提出的模型相較於其他模型具有顯著的獲利能力；當我們考慮交易成本後，所有的模型皆無法獲得超額報酬。本文提出的模型在考量非同步交易問題後，結論仍舊不變。

This paper proposes a new implied volatility function to facilitate implied volatility forecasting and option pricing. This function specifically takes the time variation in the option implied volatility into account. Our model considers the time-variant part and fits it with an asymmetric GARCH(1,1) model, so that our model contains the information in the returns of spot asset. According to our empirical results, our model substantially improves the forecasting ability and reduces the out-of-sample valuation errors in comparison with previous implied volatility functions. We conjecture that such good performance may be due to the ability of the GARCH model to simultaneously capture the correlation of volatility with spot returns and the path dependence in volatility. To test the economic significance of our model, we examine the profitability of the delta-hedged trading strategy based on various volatility models. We find that although these strategies are able to generate profits without transaction costs, their profits disappear quickly when the transaction costs are taken into consideration.