Modeling time-varying variability of asset returns with entropy

Abstract

We generalize the assumptions about the latent stochastic process of asset-return variability. Specifically, we extend GARCH models applying the Principle of Maximum Entropy. We derive the analytic form of maximum entropy distribution. Parameter estimates in time-varying variability models are sensitive to how we view variability. Under maximum entropy distribution, the higher the moment we use to define variability, the larger the likelihood value in wide range of moments. In particular, the persistence in the variability process is a nonlinear function of the moments in defining variability. These results demonstrate that the maimer to conceptualize the latent variability process can affect the problems of asset pricing such as risk-neutral density, capital asset pricing model, option prices, and value-at-risk. In conclusion, the Principle of Maximum Entropy offers an innovative framework to model the effect of asset-return variability.