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

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Fitting SPX and Vix smiles simultaneously is one of the most challenging problems in volatility modelling. A long-standing conjecture is that it may not be possible to jointly calibrate these two quantities using a model with continuous sample paths. Jim Gatheral, Paul Jusselin and Mathieu Rosenbaum present the quadratic rough Heston model as a counterexample to this conjecture. The key idea is the combination of rough volatility with a price-feedback (Zumbach) effect

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