# On VIX Futures in the rough Bergomi model

## TL;DR

This paper explores the dynamics of VIX and forward variance in the rough Bergomi model, developing efficient pricing methods for VIX derivatives and assessing its ability to jointly model VIX and SPX markets.

## Contribution

It introduces new algorithms for pricing VIX futures and options within the rough Bergomi model and evaluates its joint calibration to VIX and SPX data.

## Key findings

- The model accurately reproduces implied volatility smiles for short maturities.
- Efficient algorithms for VIX derivatives pricing are developed.
- The joint calibration demonstrates the model's capability to fit both VIX and SPX data.

## Abstract

The rough Bergomi model introduced by Bayer, Friz and Gatheral has been outperforming conventional Markovian stochastic volatility models by reproducing implied volatility smiles in a very realistic manner, in particular for short maturities. We investigate here the dynamics of the VIX and the forward variance curve generated by this model, and develop efficient pricing algorithms for VIX futures and options. We further analyse the validity of the rough Bergomi model to jointly describe the VIX and the SPX, and present a joint calibration algorithm based on the hybrid scheme by Bennedsen, Lunde and Pakkanen.