To analyse the interdependence between monetary and fiscal policy during a financial crisis, we develop an open‐economy DSGE model with monetary and fiscal policy, as well as financial markets, in a continuous‐time framework based on stochastic differential equations. Monetary policy is modelled using both a standard and a modified Taylor rule and fiscal policy is modelled as either expansionary or austere. In addition, we differentiate between open economies and monetary union members. We find evidence that the modified Taylor rule notably reduces the likelihood that the financial market crisis affects the real economy. However, if we assume that households are averse to outstanding government debt, we find that a combination of expansionary monetary policy and austerity‐oriented fiscal policy does a better job of stabilising both domestic and foreign economies in regard to both output and inflation. In the case of a monetary union, we find that stabilization of output in the country where the financial shock originated is no longer as easy and, in terms of prices, there is now deflation in that country and a positive inflation rate in the other member country of the monetary union.