The joint S&P 500/Vix smile calibration puzzle solved

SPX and Vix derivatives are modelled jointly in an arbitrage-free setting


Since Vix options started trading in 2006, many researchers have tried to build a model that jointly and exactly calibrates to the prices of Standard & Poor’s 500 options, Vix futures and Vix options. In this article, Julien Guyon solves this long-standing puzzle by casting it as a discrete-time dispersion-constrained martingale transport problem, which he solves in a non-parametric way using Sinkhorn’s algorithm

Volatility indexes, such as the Vix index, do not just

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