VIX options traded on the CBOE have become popular volatility derivatives. In this work, we bound VIX options from S\&P500 vanilla options and VIX futures. This leads us to introduce a new martingale optimal transport problem with additional constraints (that can eventually be solve numerically). Analytical lower and upper bounds are also provided, which highlight some (potential) arbitrage opportunities. We characterize the class of marginal distributions for which these explicit bounds are optimal, and illustrate numerically that they seem to be optimal also for the market-implied marginal distributions.

Joint work with P. Henry-Labordère