A multifactor transformed diffusion model with applications to VIX and VIX futures

Abstract

Transformed di¤usions (TDs) have become increasingly popular in …nancial modelling for their model ‡exibility 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 speci…ed by a ‡exible parametric stationary distribution of the observed variable. Computationally e¢ cient exact likelihood inference can be implemented for our model using a modi…ed Kalman …lter algorithm and the transformed a¢ ne 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.