Density forecasts and the leverage effect: Evidence from Observation and parameter-Driven volatility models

The leverage effect refers to the well-known relationship between returns and volatility for an equity. When returns fall, volatility increases. We evaluate the role of the leverage effect with regards to generating density forecasts of equity returns using well-known observation and parameter-driven conditional 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 specified. 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 analyzed using a large number of financial time series. For each model type, the specification with the leverage effect tends to generate more accurate density forecasts than its no-leverage counterpart. Among the specifications considered, the Beta-t-EGARCH model is the top performer, regardless of whether we attach the same weight to each region of the conditional distribution or emphasize the left tail.