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Computational Issues in the Stochastic Discount Factor Framework for Equity Risk Premium

The Stochastic Discount Factor (SDF) methodology is a general and convenient framework for asset pricing. SDF encapsulates all the modeling uncertainties and its advantage is that we do not require the knowledge of investors’ preferences. Suitable specification of SDF is, therefore, critical. It has been based on single or multiple factors and also on observable factors as well as latent factors. The variables required to proxy for the factors may be both macroeconomic as well as behavioral. In this article we show how we can incorporate such variables for empirical implementation of equity risk premium with daily frequency. Practical issues crop up to define the dependence between the asset return and the SDF. Here we show how copula can be used in this context and solve some of the analytical complexities for software implementation.