  This paper presents a novel one-factor stochastic volatility model where the
instantaneous volatility of the asset log-return is a diffusion with a
quadratic drift and a linear dispersion function. The instantaneous volatility
mean reverts around a constant level, with a speed of mean reversion that is
affine in the instantaneous volatility level. The steady-state distribution of
the instantaneous volatility belongs to the class of Generalized Inverse
Gaussian distributions. We show that the quadratic term in the drift is crucial
to avoid moment explosions and to preserve the martingale property of the stock
price process. Using a conveniently chosen change of measure, we relate the
model to the class of polynomial diffusions. This remarkable relation allows us
to develop a highly accurate option price approximation technique based on
orthogonal polynomial expansions.
