Optimal Policy of the Central Bank Under the Circumstances of Regulation of Financial Fragility

Achieving price stability and minimizing the gap in output largely depends on the stability of the financial system in the country. Maintaining financial stability is usually the role of a macroprudential regulator, however, based on the examples of past financial crises, it can be argued that a modification of monetary policy would make it more likely to avoid collapses of the financial system. In order to derive the optimal policy of monetary and macroprudential regulators in conditions of financial instability, a modification of the version of the new Keynesian model with heterogeneous households, proposed in the work of Michael Woodford (Woodford, 2012) and modified in the work of Lars Svensson (Svensson, 2012), was carried out. The modification of the model in this work consists in expanding the list of factors affecting the likelihood of a financial crisis: interest rate risk, liquidity risk and currency risk of the bank book are added to the model. In the generated model, by means of multidimensional conditional optimization, the optimal policy of the monetary regulator in the case of its benevolence and non-benevolence is explicitly derived. At the optimum, monetary policy, in the case of an endogenous probability of transition from a normal state of the economy to a crisis (depending on the listed risks associated with the functioning of the banking system), focuses on the price level in the economy, on deviation from potential output and on the marginal risk of a financial crisis with an increase in leverage, interest rate gap, liquidity gap and open currency positions, multiplied by the potential losses in case of the crisis in the next period. The optimal policy of the macroprudential regulator is also derived and the interrelation and mutual influence of monetary and macroprudential policies is proved. Based on the resulting conditions for optimal actions by regulators, recommendations are formulated regarding the implementation of monetary and macroprudential policies in conditions of financial instability.