Fear Futures: Pricing Models and Trading Strategies for VIX Futures

Abstract

Futures on the VIX volatility index are a rapidly growing asset class with important applications: they are used to hedge equity risk and to speculate on market downturns. However, there has been limited success in the literature in modeling the prices of VIX futures, as they exhibit a number of distinctive characteristics including mean reversion, normal contango, heavy-tailed distributions of returns, and strong correlations across maturities, to the VIX index, and to the S&P 500 index. There has also been little success in developing trading strategies with strong risk-adjusted returns. In this thesis, we address these two problems. First, we evaluate the performance of various VIX models applied to futures pricing. Second, we develop trading strategies which profit from the unique characteristics of the VIX futures market. In the first part of this thesis, we conduct a thorough empirical investigation of the VIX futures market to determine the criteria for a successful pricing model, analyzing the shape of the term structure of futures, the distributions of returns, and the drivers of price changes. We then evaluate the Heston stochastic variance model, the constant elasticity of variance with jumps (CEVJ) model, and the logarithmic process with jumps (LPJ) model against those criteria. Our findings are that the Heston model performs best, replicating all of the key characteristics of the VIX futures market. We also find that the CEVJ and LPJ models have two major flaws. First, they have linear pricing formulas, causing highly correlated returns across maturities. Second, they allow for positive jumps in the VIX, which leads to inflated expectations of future volatility and distributions of returns with high means and standard deviations. In the second part of this thesis, we examine VIX ETNs and trading strategies proposed in the literature which attempt to capture returns associated with roll yield. We then develop novel trading strategies which capture returns created by mean reversion and avoid the losses associated with negative roll yield, which occurs when the futures market is in contango. After simulating each of the strategies, we find that the novel strategies we create outperform existing and proposed strategies in terms of return and risk-adjusted metrics, especially in low-volatility periods.