Density Forecasts and the Leverage Effect: Some Evidence from Observation and Parameter-Driven Volatility Models

Abstract: The leverage effect refers to the well-established relationship between returns and volatility. When returns fall, volatility increases. We examine the role of the leverage effect with regards to generating density forecasts of equity returns using well-known observation and parameter-driven volatility models. These models differ in their assumptions regarding: The parametric specification, the evolution of the conditional volatility process and how the leverage effect is accounted for. The ability of a model to generate accurate density forecasts when the leverage effect is incorporated or not as well as a comparison between different model-types is carried out using a large number of financial time-series. We find that, models with the leverage effect generally generate more accurate density forecasts compared to their no-leverage counterparts. Moreover, we also find that our choice with regards to how to model the leverage effect and the conditional log-volatility process is important in generating accurate density forecasts