This paper introduces an international asset pricing model with time-varying risk premia. It augments the two factor model which has the return on the world index and trade weighted exchange rates as factors, with skewness and kurtosis factors. This leads to a stochastic discount factor that is non-linear and has time-varying factor loadings that are functions of global variables. We test this model on market indices, size and momentum sorted portfolios that are formed from stocks listed in G8 countries, as well as country-neutral size, book-to-market and momentum portfolios. Overall, the model is capable of pricing almost all sets of base assets unconditionally using only global predictive variables. It also explains much of the cross sectional variation of the country, size and momentum portfolios, and also achieves much of the substantial size and momentum premiums. The role of time-varying risk premiums that are functions of global variables is crucial to the performance of the model, particularly in the case of the exchange rate factor.