Solving asset pricing models with stochastic volatility

Abstract

This paper provides a closed-form solution for the price-dividend ratio in a standard asset pricing model with stochastic volatility. The growth rate of the endowment is a first-order Gaussian autoregression, while the stochastic volatility innovations can be drawn from any distribution for which the moment-generating function exists. The solution is useful in allowing comparisons among numerical methods used to approximate the nontrivial closed form. The closed-form solution reveals that, when using perturbation methods around the deterministic steady state, the approximate solution needs to be sixth-order accurate in order for the parameter capturing the conditional standard deviation of the stochastic volatility process to be present.