Solving models with external habit

Habit utility has been the focus of a large and growing body of literature in financial economics. This study investigates ways of accurately and efficiently solving the Campbell and Cochrane [1999. Journal of Political Economy 107, 205-251] external habit model. Solutions for this model based on a grid of values for the state variable are shown to converge as the grid becomes increasingly fine. Convergence is substantially faster if the price-dividend ratio is computed as a series of “zero-coupon equity” claims rather than as the fixed point of the Euler equation. Fitting the model to the term structure as well as to equity moments (as in [Wachter, J.A., 2005. A consumption-based model of the term structure of interest rates. Journal of Financial Economics, in press]) also results in faster convergence.