Risk Premia and Lévy Jumps: Theory and Evidence

Abstract

We develop a novel class of time-changed Lévy models which are tractable and readily applicable, capture the leverage effect, and exhibit pure jump processes with finite or infinite activity. Our models feature four nested processes reflecting market, volatility and jump risks, and observation error of time changes. To operationalize the models, we use volume-based proxies of the unobservable time changes. To estimate risk premia, we derive the change of measure analytically. An extensive time series and option pricing analysis of 16 time-changed Lévy models shows that infinite activity processes carry significant jump risk premia, and largely outperform many finite activity processes.

Keywords: Lévy jumps, time changes, tempered stable law, time series, option pricing

JEL Classification: C5, G12