General Auto-Regressive Asset Model

Abstract

Equity returns are addressed by a new General Auto-Regressive Asset Model (GARAM). In this model, two stochastic processes are employed to represent the return magnitude and return sign. Empirical auto-covariance and cross-covariance functions of the return magnitude and return sign are key model inputs, and result in a realistic structure of the clustering of volatility, dynamic asymmetry (leverage-effect), and the associated fat-tails. The term-dependence of the asset return density, including the slow decay of kurtosis and the buildup and slow decay of skewness are encompassed by GARAM. The resulting framework for unconditional and conditional Monte-Carlo simulation of asset returns is illustrated.

Keywords: asymmetry, skewness, leverage-effect, kurtosis, filtering, conditional simulation, financial time-series

JEL Classification: G11, D81