Computational Economics 15: 145–172, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands. 145 Computing Equilibria in Stochastic Finance Economies FELIX KUBLER Department of Economics, Yale University, New Haven, CT, U.S.A. KARL SCHMEDDERS Hoover Institution, Stanford University Mailing address: Department of EES/OR, Stanford University, Stanford, CA 94305-4023, U.S.A., E-mail: karl@or.stanford.edu Abstract. We describe a homotopy algorithm for the computation of equilibria in Stochastic Fi- nance Economies. The algorithm solves a nonlinear system of equations consisting of the first-order conditions of the agents’ utility maximization problems and market-clearing conditions. Moreover, we discuss the use of a straightforward homotopy approach for local comparative statics. Using our methods we evaluate price, volatility, and welfare effects of options in incomplete asset markets. Key words: incomplete markets, homotopy algorithm, index theorem, stochastic finance economy 1. Introduction Dynamic general equilibrium models with possibly incomplete markets play an important role in both modern macroeconomics and finance. While there is a considerable literature on computing equilibria for static models (see Shoven and Whalley, 1992, for an overview), little is known on computing equilibria for dy- namic models with incomplete markets and heterogeneous agents. Most of the applied literature unrealistically assumes the existence of a representative agent. We feel this assumption removes many interesting aspects of the general model. Since the equilibrium allocation is not Pareto-efficient with incomplete markets, the representative agent is fictional and it becomes impossible to interpret the results of models employing such an agent in a general equilibrium framework (see Kirman, 1992, for a more general criticism of representative agent analysis). However, computing equilibria for multi-period general equilibrium models with incomplete markets and heterogeneous agents is a difficult task. The first prob- lem arises because the model is often formulated as an infinite horizon economy (see Lucas, 1978; or Hernandez and Santos, 1996, for a version of the Lucas asset pricing model with several agents). While this formulation actually simplifies the analysis in a representative agent framework, it introduces many technical difficul- ties for models with several agents. Duffie et al. (1994) shows that the state space