A Toolkit for Pricing Assets in Nonlinear Dynamic Stochastic Models Easily

Harald Uhlig
CentER for Economic Research, Tilburg University
Uhlig@kub.nl

Abstract

This paper provides a toolkit for pricing assets in nonlinear economic dynamic discrete-time models easily. Much of modern macroeconomic research is focussed on analyzing such models and deriving its implications. Among the most important implications are those for asset pricing relationships, but calculating them can often be painful. This paper aims at easing this pain. Building on a companion paper, it considers an approximate solution to the model, stated as a loglinear recursive equilibrium law of motion. Similarly, the Lucas asset pricing relationship can be loglinearized. However, the resulting recursive loglinear asset pricing law can easily require more lags than required for stating the solution of the underlying model, thus complicating the task of pricing these assets. While one could simply ``mechanically'' enlarge the state space in the underlying model to take care of these longer lags, the derived solutions become less intuitive and furthermore require solving a new version of the model each time an asset of a different payoff structure is introduced. This paper thus instead takes a given equilibrium law of motion and shows how the asset pricing law of motion can be derived from it. Examples are given.