A regime switching quadratic model for VIX futures valuation

We develop a continuous time model for the VIX futures valuation. In this model, the state variable follows a mean-reverting process and the logarithm of future price is a quadratic function of state variable with regime switching mean. The transition between regimes is governed by a continuous time Markov chain. We provide analytical solutions for future prices and show how the regime shifts and the nonlinearity introduced by the quadratic term affect the term structure of future prices. We estimate both single regime and regime switching models through the Kalman filter. In our empirical work, we document that, indeed, the regime switching quadratic model can improve the forecasting power of the existing models.