Pricing of the Time-Change Risks

Abstract

We develop a discrete-time real endowment economy featuring recursive preferences and a Levy time-change subordinator, which represents a clock that connects business time to calendar time. This setup provides a convenient equilibrium framework for pricing non-Gaussian risks, with closed-form analytical solutions for the asset prices. We show that the non-Gaussianity of fundamentals due to time-deformation induces risk compensations which depend on higher order moments of consumption and dividend series. Persistence of the activity shocks leads to predictability of the endowment streams and time variation in asset prices and risk premia. In numerical calibrations, we show that the compensation for Levy risks accounts for about one-third of the overall risk premium in the economy.

Keywords: Risk premium, time change, Levy processes, recursive preferences

JEL Classification: G12, D51, C51