Abstract: This paper shows how to recover stochastic volatility models (SVMs) from market models of the VIX futures term structure. Compared with SVMs, market models have more flexibility for fitting the VIX term structure, and therefore are better suited for pricing VIX derivatives. But the VIX itself is a derivative of the S&P500 index (SPX) and it is common practice to price SPX derivatives using an SVM. In this talk I will present a method for the recovery of a stochastic volatility function as the output of an inverse problem where the inputs are given by a VIX market model. Analysis will show that some conditions need to be met in order to avoid inter-model arbitrage. Several models are analyzed and explored numerically to gain a better understanding of the theory and its limitations.