Historical Analysis of Rough Volatility Models to the SPX Market

Abstract

We perform a historical analysis of selected rough volatility models to the SPX market. Tailoring the neural network pricing method of [27] to our needs, we train neural networks for the rough Heston model from [14], the rough Bergomi model from [4] as well as an extended version of the latter. As a benchmark we include also the classical Heston model from [24]. Calibrating the models across 15 years of historical SPX options prices we first and foremost document consistently superior results using rough volatility. Comparing rough Heston and rough Bergomi we also find that while the former model calibrates slightly better, the latter model produces more robust predictions. Our calibration results also illuminate a structural problem in that both of these models (on average) produces too little curvature at short expirations, too little skew at long expirations. Using an extended rough Bergomi model where the explosion rates of smile and skew are decoupled, did not resolve this problem.