English

The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem

Mathematical Finance 2020-01-08 v1

Abstract

Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may not be possible to calibrate jointly these two quantities with a model with continuous sample-paths. We present the quadratic rough Heston model as a counterexample to this conjecture. The key idea is the combination of rough volatility together with a price-feedback (Zumbach) effect.

Keywords

Cite

@article{arxiv.2001.01789,
  title  = {The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem},
  author = {Jim Gatheral and Paul Jusselin and Mathieu Rosenbaum},
  journal= {arXiv preprint arXiv:2001.01789},
  year   = {2020}
}