A Multi-Factor Transformed Diffusion Model with Applications to VIX and VIX Futures

Transformed diffusions (TDs) have become increasingly popular in financial modelling for their model flexibility and tractability. While existing TD models are predominately one-factor models, empirical evidence often prefers models with multiple factors. We propose a novel distribution-driven nonlinear multi-factor TD model with latent components. Our model is a transformation of a underlying multivariate Ornstein Uhlenbeck (MVOU) process, where the transformation function is endogenously specified by a flexible parametric stationary distribution of the observed variable. Computationally efficient exact likelihood inference can be implemented for our model using a modified Kalman filter algorithm and the transformed affline structure also allows us to price derivatives in semi-closed form. We compare the proposed multi-factor model with existing TD models for modelling VIX and pricing VIX futures. Our results show that the proposed model outperforms all existing TD models both in the sample and out of the sample consistently across all categories and scenarios of our comparison.