The Price of Higher Order Catastrophe Insurance: The Case of VIX Options

We develop equilibrium pricing model for VIX options aimed at explaining observed characteristics in the data. The model is based on a long-run-risk formulation with Duffie- Epstein preferences in an economy with stochastic volatility and volatility jumps. Our VIX model is a special case of a more general and tractable continuous-time asset pricing frame- work featuring a recursive preference structure for a representative agent in an economy with affine jump-diffusion states. The framework is greatly useful in the sense that it can be readily used to price any assets with state-variable-dependent payoffs, quite general as it encompasses several recent work as special cases, and highly tractable in the sense that the state-price density and thus every price can be solved out exactly in an semi-analytical form. Specifically, we derive semi-closed form solutions for options prices using Fourier in- version techniques. Our VIX options pricing model fit many of the observed characteristics of the data, including right skewness, concave implied volatility functions, and potentially large negative average rates of return to ATM and OTM VIX call options.