Empirical analysis of rough and classical stochastic volatility models to the SPX and VIX markets

We conduct an empirical analysis of rough and classical stochastic volatility models to the SPX VIX options markets. Our focusses primarily on calibration quality is split in two parts. In part one, we perform a historical over years 2004–2019 selection that include one-factor Bergomi Heston models. two, consider three dates with low, typical, high volatility, examine wide models, calibrate both as well jointly options. The key results are follows: fail create term structure smile effect sufficiently pronounced for Moreover, discover short-expiry smiles generally more symmetric than long-expiry smiles, feature neither find these can reproduce. propose alternative model driven by Ornstein-Uhlenbeck processes uses non-standard transformation function. Calibrating it options, obtain almost perfect fits, calibrating very decent fits. This suggests, contrary what one might be led believe based much existing literature, joint SPX-VIX problem largely solvable two-factor all without roughness jumps.