A Comparative Study of Equilibrium Equity Premium under Discrete Distributions of Jump Amplitudes

Abstract

In this paper, we compare equilibrium equity premium under discrete distributions of jump amplitudes. In particular, we consider the binomial and gamma distributions because of their applicability in finance. For the binomial, we assume that the price movement is allowed to either increase or decrease with probability p or 1 − p respectively. n is the trading period thereby forming a vector x of jump sizes (shifts) whose distribution is a binomial over time. For the gamma, the jumps are taken to be rare events following a Poisson distribution whose waiting times between them follows a gamma. In both distributions, the optimal consumption of the investor is affected by the deterministic time preference function y (t ) but it has no effect on the diffusive and rare-events premia thereby not affecting the equilibrium equity premium. Also, for n, k = 0 , the volatility effect on the equity premium is the same in both the power and square root utility functions although the equity premium is not affected by the wealth process V (t ) . However, the wealth process affects the equity premium of the quadratic utility fuction. We observe no significant differences in equity premium for the two discrete distributions.