In this paper we examine and compare the performance of a variety of continuous-
time volatility models in their ability to capture the behaviour of the VIX. The `3/2-
model' with a di®usion structure which allows the volatility of volatility changes to be
highly sensitive to the actual level of volatility is found to outperform all other popular
models tested. Analytic solutions for option prices on the VIX under the 3/2- model are
developed and then used to calibrate at-the-money market option prices.