General Equilibrium Asset Pricing Under Regime Switching
Communications on Stochastic Analysis, 2, 2008.
26 Pages Posted: 18 Mar 2007 Last revised: 10 Feb 2018
Date Written: March 12, 2007
In this paper, we have developed a continuous time general equilibrium model in an economy which has two states, a 'good' state and a 'bad' state. There are two types of shocks in the economy: small shocks and large shocks. The small shocks which only affect the individual price movements are modeled by Brownian motions. The large shocks, the states of the economy, are modeled by a continuous time Markov Chain. There are one riskless assets, n basic risky assets and contingent claims written on the risky assets in the market. The states of the economy affect the expected returns and the variances of the assets. We assume in different states, the means and variances of the instantaneous returns are different. We then investigate the asset pricing problem in general equilibrium with a representative agent who maximizes a cost function. Based on the assumption of a CRRA utility function, we have derived a partial differential equation satisfied by the representative agent's cost function. A form of the solution of the partial differential equation has been given in general equilibrium with intermediate consumption. In the case when the representative agent doesn't have intermediate consumption, we have found an explicit solution of the cost function. A closed-form expression for the riskless interest rate has been derived. We have also provided a partial differential equation satisfied by any contingent claim written on basic risky asset. The stochastic discount factor has been defined and computed in our framework. Based on the stochastic discount factor, we have provided an explanation for the equity premium puzzle.
Keywords: General Equilibrium, Representative Agent, Utility Function, Regime Switching, Stochastic Discount Factor, Equity Premium Puzzle
JEL Classification: D50, G12
Suggested Citation: Suggested Citation