We analyze the relationship between the exchange markets and the integration process of the Latin American stock markets (MILA), focusing the analysis on two points. First, we evaluate the existence and nature of exchange risk premium and its relationship with the uncovered interest parity (UIP) bias. Second, we analyze the effect of MILA on Latin American foreign exchange markets. We use monthly time series between January 1997 and December 2021 for the exchange markets of Brazil, Chile, Colombia, Mexico and Peru. The econometric analysis was based on OLS, GARCH-in-Mean and DCC-MGARCH regressions. Our results indicate that UIP is does not meet. Even the GARCH-in-Mean models results indicates that there is no individual risk premium that corrects UIP bias. However, the results of the DCC-MGARCH model show that there is a risk premium generated simultaneously by the correlation between markets. Finally, MILA increased the dynamic correlations of exchange returns and risk premiums, mainly among the MILA markets. These results have relevant implications for policymakers and investors due to the impacts on exchange markets dependence and international investment decision-making.