  The quintic Ornstein-Uhlenbeck volatility model is a stochastic volatility
model where the volatility process is a polynomial function of degree five of a
single Ornstein-Uhlenbeck process with fast mean reversion and large
vol-of-vol. The model is able to achieve remarkable joint fits of the SPX-VIX
smiles with only 6 effective parameters and an input curve that allows to match
certain term structures. We provide several practical specifications of the
input curve, study their impact on the joint calibration problem and consider
additionally time-dependent parameters to help achieve better fits for longer
maturities going beyond 1 year. Even better, the model remains very simple and
tractable for pricing and calibration: the VIX squared is again polynomial in
the Ornstein-Uhlenbeck process, leading to efficient VIX derivative pricing by
a simple integration against a Gaussian density; simulation of the volatility
process is exact; and pricing SPX products derivatives can be done efficiently
and accurately by standard Monte Carlo techniques with suitable antithetic and
control variates.
