New frontiers for arch models

Abstract In the 20 years following the publication of the ARCH model, there has been a vast quantity of research uncovering the properties of competing volatility models. Wide‐ranging applications to financial data have discovered important stylized facts and illustrated both the strengths and weaknesses of the models. There are now many surveys of this literature. This paper looks forward to identify promising areas of new research. The paper lists five new frontiers. It briefly discusses three—high‐frequency volatility models, large‐scale multivariate ARCH models, and derivatives pricing models. Two further frontiers are examined in more detail—application of ARCH models to the broad class of non‐negative…