An equilibrium asset pricing model based on Levy processes: relations to stochastic volatility, and the survival hypothesis

This paper presents some security market pricing results in the setting of a security market equilibrium in continuous time. The model consists in rel axing the distributional assumptions of asset returns to a situation where the underlying random processes modeling the spot prices of assets are expo nentials of Levy processes, the latter having normal inverse Gaussian margi nals, and where the aggregate consumption is inverse Gaussian. Normal inver se Gaussian distributions have proved to fit stock returns remarkably well in empirical investigations. Within this framework we demonstrate that cont ingent claims can be priced in a preference-free manner, a concept defined in the paper. Our results can be compared to those emerging from stochastic volatility models, although these two approaches are very different. Equil ibrium equity premiums are derived, and calibrated to the data in the Mehra and Prescott [J. Monetary Econ. 15 (1985) 145] study. The model gives a po ssible resolution of the equity premium puzzle. The "survival" hypothesis o f Brown et al. [J. Finance L 3 (1995) 853] is also investigated within this model, giving a very low crash probability of the market. (C) 2000 Elsevie r Science B.V. All rights reserved.