The quintic Ornstein-Uhlenbeck model for joint SPX and VIX calibration

A new model that jointly fits the smiles of VIX and SPX is presented


Eduardo Abi Jaber, Camille Illand and Shaun (Xiaoyuan) Li present a simple model to jointly fit the SPX-VIX smiles with only six effective parameters and an input curve that allows matching of certain term structures. The model remains tractable for pricing and calibration: the VIX squared is polynomial in the Ornstein-Uhlenbeck process, leading to efficient VIX derivative pricing by a simple integration with respect to a Gaussian density. Simulation of the

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