The Research about Implied Volatility Function for Taiwan Stock Index Option

[[abstract]]本文利用2002年至2009年，台灣期貨交易所的台指選擇權與台指期貨資料，計算出台指選擇權的隱含波動率，並利用選擇權的價性指標與距到期期間來做隱含波動率函數的配適。價性指標包括傳統價性指標，也就是將執行價格除以標的資產價格，以及將傳統價性指標取自然對數兩種；而標的資產則分為指數現貨與指數期貨兩種。我們的研究結果發現：1 台指選擇權確實存在微笑波動現象。2 價性指標以取自然對數的模式較佳，對隱含波動率的解釋能力較高。3 距到期期間與隱含波動率大致呈現線性關係。4 價內與價外的隱含波動現象並不對稱。無論買權或賣權，價內選擇權隱含波動率對價性指標較為敏感，也就是斜率較陡，但是曲率的大小則不具一致性。[[abstract]]We determined the implied volatilities of Taiwan stock index options (TXO) by collecting the price data of TXO and Taiwan stock index futures (TX) from 2002 to 2009 and fitted the implied volatilities as a function of moneyness index and time to expiration We used two kinds of functions the traditional one which divided exercise price by underlying price and the natural logarithm of the traditional function to determine moneyness index We also used two kinds of underlyings the spot index and the index futures We found considering volatilities of TXO：1 Volatility smile does exist 2 Taking natural logarithm of the traditional moneyness index can improve the goodness of fit of volatility function 3 Implied volatility is almost a linear function of options’ duration 4 Volatility smile is asymmetric to moneyness In-the-money implied volatility is more sensitive to moneyness index than out-of-the-money implied volatility regardless call or put The slope of in-the-money implied volatility to moneyness index is steeper than the one of out-of-the-money The curvatures do not have a consistent resul