Under a currency board, the central bank relinquishes control over its monetary policy and domestic interest rates converge towards the foreign rates. Nevertheless, a spread between both usually remains. This spread can be persistently positive due to elevated risk in the economy. This paper models that feature by building a DSGE model with a currency board, where the domestic interest rate is endogenously derived as a function of the foreign rate, the external debt position and an exogenous risk premium component. Time variation in the volatility of the risk premium component is then modelled via a Markov-switching component. Estimating the model with Bayesian methods and Estonian data shows that the economy does not react much to shocks to domestic interest rates in quiet times but is much more sensitive during crises, and matches the financial and banking crises, which cannot be captured by the standard DSGE model.