The Chicago Board Options Exchange introduced the Market's Volatility Index (VIX) in 1993. It is a financial instrument which uses Standard & Poor's 500 Index options to measure market volatility. The first VIX derivatives were introduced in 2004. We are interested in modeling these derivatives. After observing mean regressing characteristics of the VIX derivatives, we use the Ornstein-Uhlenbeck process to model these derivatives. We then implement two different methods to estimate the model's parameters using daily market data. We compare the modeling accuracy of an Ornstein-Uhlenbeck process with a geometric Brownian motion model. Our results confirm the Ornstein-Uhlenbeck process can model VIX derivatives more accurately than a geometric Brownian motion.
We show it is possible to model VIX derivatives with reasonable accuracy looking one month forward. Our results can potentially aid investors using volatility derivatives and influence strategies to hedge against risk.