In this paper we present an exact maximum likelihood treatment for the estimation of a Stochastic Volatility in Mean (SVM) model based on Monte Carlo simulation methods. The SVM model incorporates the unobserved volatility as an explanatory variable in the mean equation. The same extension is developed elsewhere for Autoregressive Conditional Heteroskedastic (ARCH) models, known as the ARCH in Mean (ARCH-M) model. The estimation of ARCH models is relatively easy compared with that of the Stochastic Volatility (SV) model. However, efficient Monte Carlo simulation methods for SV models have been developed to overcome some of these problems. The details of modifications required for estimating the volatility-in-mean effect are presented in this paper together with a Monte Carlo study to investigate the small-sample properties of the SVM estimators. Taking these developments of estimation methods into account, we regard SV and SVM models as practical alternatives to their ARCH counterparts and therefore it is of interest to study and compare the two classes of volatility models. We present an empirical study about the intertemporal relationship between stock index returns and their volatility for the United Kingdom, United States and Japan. This phenomenon has been discussed in the financial literature but has proved hard to find empirically; we find evidence of a negative but weak relationship. <BR><BR>
