Abstract
VIX options traded on the CBOE have become popular volatility derivatives. As SP500 vanilla options and VIX both depend on S&P500 volatility dynamics, it is important to understand the link between these products. In this paper, we bound VIX options from vanilla options and VIX futures. This leads us to introduce a new martingale optimal transportation problem that we solve numerically. Analytical lower and upper bounds, proved to be optimal for a large class of marginal distributions, are also provided which already highlight some arbitrage opportunities. We illustrate numerically that these bounds seem to be optimal for a larger class of marginal distributions.
The paper is available on SSRN.