We propose a model to capture the dynamics of asset returns, with periods of crises that are characterized by contagion. In the model, a jump in one region of the world increases the intensity of jumps both in the same region (self-excitation) as well as in other regions (cross-excitation), generating episodes of highly clustered jumps across world markets that mimic the observed features of the data. We develop and implement moment-based estimation and testing procedures for this model. The estimates provide evidence of self-excitation both in the US and the other world markets, and of asymmetric cross-excitation, with the US market typically having more influence on the jump intensity of other markets than the reverse. We propose filtered values of the jump intensities as a measure of market stress and examine their out-of-sample forecasting abilities.

This paper explores the optimal consumption and investment behavior of an individual who derives utility from the ratio between his consumption and an endogenous habit. We obtain closed-form policies under general utility functionals and stochastic investment opportunities by developing a nontrivial linearization to the budget constraint. This enables us to explicitly characterize how habit formation affects the marginal propensity to consume and optimal stock–bond investments. We also show that in a setting that combines habit formation with Epstein–Zin utility, consumption no longer grows at unrealistically high rates at high ages and investments in risky assets decrease.