  In this paper we introduce a simple continuous-time asset pricing framework,
based on general multi-dimensional diffusion processes, that combines
semi-analytic pricing with a nonlinear specification for the market price of
risk. Our framework guarantees existence of weak solutions of the nonlinear
SDEs under the physical measure, thus allowing to work with nonlinear models
for the real world dynamics not considered in the literature so far. It emerges
that the additional flexibility in the time series modelling is econometrically
relevant: a nonlinear stochastic volatility diffusion model for the joint time
series of the S&P 100 and the VXO implied volatility index data shows superior
forecasting power over the standard specifications for implied and realized
variance forecasting.
