Volatility and dynamic dependence modeling: Review, applications, and financial risk management

Since the introduction of ARCH models close to 40 years ago, a wide range of models for volatility estimation and prediction have been developed and integrated into asset allocation, financial derivative pricing, and financial risk management. Research has also been very active in extending volatility modeling to dependence modeling and in developing our understanding of risk and uncertainty in financial systems. This paper presents a review on the statistical modeling on volatility and dynamic dependence of financial returns. In addition, we present a real data example using a time‐varying copula model to estimate the dynamic dependence of stock returns. Research on volatility and dynamic dependence modeling will continue to encounter statistical and computational challenges; it is necessary to persist in dealing with the 3H (high dimension, high frequency, high complexity) paradigm in modeling.