This paper explores the implementation of an intertemporal asset pricing model with stochastic volatility. This model is applied to equity asset pricing at the Nairobi Securities Exchange (NSE) and the Johannesburg Stock Exchange (JSE). The return on the aggregate stock market is modelled using a vector auto regression (VAR) model and the volatility of all shocks to the VAR is modelled using GARCH and EGARCH models. It is shown that the reduced form of the ICAPM with stochastic volatility is inadequate in the context of equity asset pricing at the NSE and JSE. However, the variables indicate the existence of a significant relationship between asset returns and realized market variance and PE ratios to motivate further research
