  The paper demonstrates that a pure-diffusion 3/2 model is able to capture the
observed upward-sloping implied volatility skew in VIX options. This
observation contradicts a common perception in the literature that jumps are
required for the consistent modelling of equity and VIX derivatives. The
pure-diffusion model, however, struggles to reproduce the smile in the implied
volatilities of short-term index options. One remedy to this problem is to
augment the model by introducing jumps in the index. The resulting 3/2 plus
jumps model turns out to be as tractable as its pure-diffusion counterpart when
it comes to pricing equity, realized variance and VIX derivatives, but
accurately captures the smile in implied volatilities of short-term index
options.
