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

2020/01/06 by Jim Gatheral, Gatheral, Jim, Paul Jusselin +3 · 3 citations
Engineering · Materials Science · #3D Shape Modeling and Analysis #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Textile materials and evaluations

paper · pdf · doi:10.48550/arxiv.2001.01789

openalex publication_date 2020/01/06 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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.

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