Pricing VIX futures: A framework with random level shifts

We propose a DRLS framework to price VIX futures by modeling the logVIX series dynamics using the ARFIMA and HAR models that introduce the random level shifts component. Compared with other traditional time series models, our model allows the change of the theoretical mean value of the VIX index by time, which is more reasonable since there are different volatility states under different market environments. Using the Kalman filter, we can derive the explicit formula of the VIX futures price without calculating numerical integration that is different from models without random level shifts. The empirical results show that the DRLS framework performs better in both in-sample estimating and out-of-sample forecasting than directly pricing models without random level shifts and is much simpler.