the VIX is by definition the square root of the variance swap rate implied by SPX options current VIX futures (with maturity T) prices are between the forward volatility swap rate and the forward-variance swap rate over the period (T,T+30/365). The instantaneous variance of SPX , V(t), is a linear function of the square of VIX.
At the risk of giving myself more competition (yeah right, who here is gonna implement this?) http://cermics.enpc.fr/~guyon/docum...nPuzzleSolved_Slides_QuantMinds_15May2019.pdf https://poseidon01.ssrn.com/deliver...3118106107066080074103087120090119024&EXT=pdf https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3397382
I cant handle the high-resolution video. Too many damn pixels that arent porn freaks me out. https://arxiv.org/abs/2001.01789 The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem Jim Gatheral, Paul Jusselin, Mathieu Rosenbaum 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.