An equilibrium asset pricing model based on Lévy 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 relaxing the distributional assumptions of asset returns to a situation where the underlying random processes modeling the spot prices of assets are exponentials of Lévy processes, the latter having normal inverse Gaussian marginals, and where the aggregate consumption is inverse Gaussian. Normal inverse Gaussian distributions have proved to fit stock returns remarkably well in empirical investigations. Within this framework we demonstrate that contingent 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. Equilibrium 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 possible resolution of the equity premium puzzle. The “survival” hypothesis of Brown et al. [J. Finance L 3 (1995) 853] is also investigated within this model, giving a very low crash probability of the market.