VIX Options in the Short-Maturity Regime

We derive the short-maturity asymptotics for VIX option prices in local-stochastic volatility models. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. Using large deviations theory methods, the asymptotics for the OTM options are expressed as a two-dimensional variational problem, which is reduced to an extremal problem for a function of two real variables. This extremal problem is solved explicitly in an expansion in log-moneyness. We will study the VIX option pricing for Heston-type model and the SABR model in more detail. Finally, we will discuss VIX option pricing in the presence of jumps. This is based on the joint work with Desen Guo, Dan Pirjol and Xiaoyu Wang.