Continuous trading in an exchange economy under discontinuous dynamics: A resolution of the equity premium puzzle

This paper analyses asset prices, the term structure of the interest rate, the spot price of risk and derives the equilibrium excess returns on risky assets in an exchange economy where the underlying exogenous uncertainty is a pure multidimensional jump process. We derive closed-form solutions for the interest rate and the risk premiums on risky assets, as well as prices of derivative assets for a general class of separable utility indices and endowment processes. Our analysis demonstrates that when the underlying jumps of the aggregate consumption process are not negligible, then the traditional form of the consumption-based capital asset pricing model need not hold and the asset risk premiums may be larger than predicted by the traditional CCAPM in continuous time, based on Itô-diffusion processes. Our alternative model for the equity premiums lends itself to possible empirical testing. We also demonstrate that a more traditional consumption-based capital asset pricing type model approximately results when the jump sizes in the aggregate consumption are small. Our analysis suggests an explanation for the large estimates of the risk premiums reported in empirical tests of the single beta CCAPM. The analytical tool used is stochastic calculus for random point processes represented by random measures.