VIX Term Structure in the Rough Heston Model via Markovian Approximation

Abstract

We model the VIX term structure using the rough Heston model. Since the direct numerical modeling of the rough Heston model is computationally inefficient, we adopt a Markovian approximation approach. Building on the Markovian framework, we eliminate the need for simulation by exploiting an analytical expression for VIX. The resulting formula for squared VIX under the Markovian approximation provides an analytical approximation to its counterpart under the rough Heston model. Another efficiency in the calibration procedure is achieved by exploiting the analytical gradient formulas of squared VIX. Empirically, using an extensive dataset of daily VIX term structures, we show that the rough Heston model outperforms various competing Heston-type models with jumps in both in-sample and out-of-sample fit and yields more reliable estimates of spot volatility, validating that rough volatility is preferred to jumps in modeling VIX term structure.