Modeling VXX Price

We study the VXX Exchange Traded Note (ETN) that has been actively traded on the New York Stock Exchange in recent years (Whaley, 2013). We confirm the puzzling phenomenon of the significantly negative returns of the VXX that has been reported in the literature. Using the VIX futures pricing framework from Zhang and Zhu (2006) and Zhang, Shu, and Brenner (2010), we create, to our knowledge, the first model of the VXX price which accounts for the fundamental underlying relationships of the SPX (S&P 500 index), the VIX and the VXX. Using our model of the VXX price, we quantify the roll yield and show that the returns of the VXX are driven by the roll yield, as proposed in the literature. The roll yield of any futures position is the return of the position that is not due to movements in the underlying; it is often called the cost of carry in other futures markets. We then show that the sign of the roll yield of the VXX is, on aggregate, driven by the market price of variance risk. We provide a new simple and robust methodology for estimating the market price of variance risk using our model and inputting VXX price. This has to be estimated for any affine model of the SPX which uses a stochastic volatility process, as in the Heston (1993) framework. Our VXX model could be used to price options written on the VXX