Chasing Volatility: A Persistent Multiplicative Error Model with Jumps

Abstract

The realized volatility of financial returns is characterized by persistence and occurrence of unpredictable large increments. To capture those features, we introduce the Multiplicative Error Model with jumps (MEM-J). When a jump component is included in the multiplicative specification, the conditional density of the realized measure is shown to be a countably infinite mixture of Gamma and K distributions. Strict stationarity conditions are derived. A Monte Carlo simulation experiment shows that maximum likelihood estimates of the model parameters are reliable even when jumps are rare events. We estimate alternative specifications of the model using a set of daily bipower measures for 7 stock indexes and 16 individual NYSE stocks. The estimates of the jump component confirm that the probability of jumps dramatically increases during the financial crises. Compared to other realized volatility models, the introduction of the jump component provides a sensible improvement in the fit, as well as for in-sample and out-of-sample volatility tail forecasts.

Keywords: Multiplicative Error Model with Jumps, Jumps in volatility, Realized measures, Volatility-at-Risk

JEL Classification: C22, C58, G10