Affine General Equilibrium Models

Abstract

No-arbitrage models are extremely flexible modelling tools, but often lack economic motivation. This paper describes an equilibrium consumption based CAPM framework based on Epstein-Zin preferences, which produces analytic pricing formulas for stocks and bonds under the assumption that macro growth rates follow affine processes. This allows the construction of equilibrium pricing formulas while maintaining the same flexibility of state dynamics as in no-arbitrage models. In demonstrating the approach, the paper presents a version of the Bansal & Yaron (2004) model which maintains a positive volatility process, as well as an example in which the volatility process is allowed to jump. The latter produces endogenous asset stock market crashes as stock prices drop to reflect a higher expected rate of return in response to increased risk. A third generalization is a model of nominal stock and bond prices. The nominal yield curve in this model has positive slope if expected inflation growth negatively impacts real growth. This model also produces asset prices that are consistent with observed data, including a substantial equity premium at moderate levels of risk aversion.

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