Expected Utility Theory on General Affine GARCH Models

Abstract

Expected utility theory has produced abundant analytical results in continuous-time finance, but with very little success for discrete-time models. Assuming the underlying asset price follows a general affine GARCH model which allows for non-Gaussian innovations, our work produces an approximate closed-form recursive representation for the optimal strategy under a constant relative risk aversion (CRRA) utility function. We provide conditions for optimality and demonstrate that the optimal wealth is also an affine GARCH. In particular, we fully develop the application to the IG-GARCH model hence accommodating negatively skewed and leptokurtic asset returns. Relying on two popular daily parametric estimations, our numerical analyses give a first window into the impact of the interaction of heteroscedasticity, skewness and kurtosis on optimal portfolio solutions. We find that losses arising from following Gaussian (suboptimal) strategies, or Merton's static solution, can be up to 2.5% and 5%, respectively, assuming low-risk aversion of the investor and using a five-years time horizon.

Bayesian Learning in an Affine GARCH Model with Application to Portfolio Optimization

“…Nonetheless, to the best of our knowledge, there is no study in the literature addressing GARCH models in portfolio optimization and parameter errors via Bayesian analysis. The Affine GARCH model, pioneered by [23], which permits closed-form pricing of options, has led to recent analytical results within EUT; see [24,25] for extensions to other Affine GARCH models. In these works, the authors did not account for parameter uncertainty.…”