The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem
11 Pages Posted: 31 Jan 2020
Date Written: January 6, 2020
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: SPX smiles, VIX smiles, rough Heston model, Zumbach effect, quadratic rough Heston model, Guyon's conjecture
JEL Classification: G13
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