本篇論文主要研究隱含遠期波動率與實際的波動率之間的關係。我們利用期貨的概念，加入選擇權當作標的物，建構出對未來選擇權作計算的公式。利用此一公式所計算出了選擇權價格，套入Black-Scholes訂價公式，反推出未來的波動率。Black-Scholes訂價公式的其中一個因子是執行價格，所以不同的執行價格，會有不同的隱含波動率，利用單一執行價格的隱含波動率去預測未來的波動率，會有很大的誤差，為了克服這樣的問題，我們利用芝加哥期權交易所(CBOE)的免模型的概念，推算出每天的隱含波動率。
實證結果可知，利用我們建構之新的未來選擇權計算公式，加上利用免模型推算出的隱含波動率，對於預測未來的波動率有顯著的結果。並且台灣股票指數選擇權的結果較標準普爾500 指數選擇權顯著。

The purpose of this paper is to investigate the relationship between implied forward volatility and actual volatility. We used the concept of futures, adding the option as the underlying asset, to construct the formula of forward option price. Using this formula we have calculated the option price, and derived the implied forward volatility by Black-Scholes pricing formula. We then try to predict actual volatility by using the implied forward volatility. However, the result is not significant. The reason is that one factor of the Black-Scholes pricing formula is the strike price, therefore using different strike prices will lead to different implied forward volatility. Using the implied forward volatility of a single strike price to predict the daily volatility is not accurate. In order to overcome this problem, we used the model-free concept launch by Chicago Board Options Exchange (CBOE) to calculate the daily implied forward volatility.
From the empirical results, we find that using the forward option formula and the implied forward volatility calculated by model-free conception is better than the Black-Scholes pricing formula. The result of Taiwan Stock Index Options is more significant than Standard & Poor 500 Index Options.

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