Abstract
In this paper, we first develop a theoretical and model-free VXX formula in terms of Volatility Index (VIX) futures in both discrete and continuous forms. The discrete form of VXX can quantify the roll yield of VXX, which can be used to explain VXX's underperformance. Using the log-normal Ornstein-Uhlenbeck (LOU) diffusion model, we show how the number of rolls of VIX futures affects the VXX option pricing formula and its implied volatility (IV). To further verify the nonflat IV of VXX, the VXX option pricing formula under the LOU with stochastic volatility model is also derived. Finally, we analyze their pricing performance, and the ability to forecast implied volatilities.