Abstract
We introduce a new pricing formula on forward options, and we add the concept of futures whose underlying asset is an option. Under the assumption of no-arbitrage, we use two options of different maturities to get the price of the forward option. Then, we put relative parameters into Black-Scholes pricing formula, getting the volatility which is so-called the implied forward volatility. After computing the implied forward volatility from the formula of forward options, we will use data of VIX futures to make comparison. We also compare with forward volatility and examine the predictability of it.