Abstract
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.