Closed-form portfolio optimization under GARCH models

This paper develops an approximate closed-form optimal portfolio allocation formula for a spot asset whose variance follows GARCH(1,1) process. We consider investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected from terminal wealth under Heston and Nandi (2000) GARCH (HN-GARCH) model. Based on approximation of log returns Campbell Viceira (1999), we obtain closed formulas investment strategy, value function wealth. find strategy is independent development risky asset, solution converges that continuous-time stochastic volatility model (Kraft, 2005), albeit additional conditions. For daily trading scenario, solutions are quite robust variations in parameters, while numerical equivalent loss (WEL) analysis shows good performance solution, inferior Merton solution.The extended two dimensions multivariate affine Escobar-Anel et al. (2020).