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 but it has no effect on the diffusive and rare-events premia thereby not affecting the equilibrium equity premium. Also, for , 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 . 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.
Highlights
The equity risk premium or equity premium, the rate by which risky stocks are expected to outperform safe fixed-income investments, such as government bonds and bills, is perhaps the most important index in finance
Jump diffusion has been widely explored in the area of option pricing but little work has been done to ascertain the behaviour of equity premium under jump diffusion models
If X is a vector of binomially distributed jump sizes, an investor’s equilibrium equity premium with
Summary
The equity risk premium or equity premium, the rate by which risky stocks are expected to outperform safe fixed-income investments, such as government bonds and bills, is perhaps the most important index in finance. We derive numerical formulae for an equity premium and simulate graphs by imposing a Binomial distribution on the jump sizes. [1]-[4] studied the Pricing of Options under Jump-Diffusion Processes, and derived the appropriate characterization of asset market equilibrium when asset prices follow jump-diffusion process. They developed the general methodology for pricing options on such assets. The model proposed by [5] incorporated the early exercise feature of American options as well as arbitrary jump distributions. This paper is related to a number of papers including [11] [18]-[24] solved for the equity premium in an economy with a robust agent that has recursive utility
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