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The paper demonstrates that a pure-diffusion 3/2 model is able to capture theobserved upward-sloping implied volatility skew in VIX options. Thisobservation contradicts a common perception in the literature that jumps arerequired for the consistent modelling of equity and VIX derivatives. Thepure-diffusion model, however, struggles to reproduce the smile in the impliedvolatilities of short-term index options. One remedy to this problem is toaugment the model by introducing jumps in the index. The resulting 3/2 plusjumps model turns out to be as tractable as its pure-diffusion counterpart whenit comes to pricing equity, realized variance and VIX derivatives, butaccurately captures the smile in implied volatilities of short-term indexoptions.

Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model