The emergence of a market risk due to performing operations with currency can result in substantial financial losses. That is why such situations require carrying out of profound analysis and management of respective risks. The market risk of this kind is characterized with possible losses of financial resources due to incorrectly performed operations with currency. The paper considers the possibility of application of the VaR methodology to the bank currency portfolio: delta-normal, as well as the methods of historical modeling and Monte Carlo simulation. As a result of performing the computational experiments with the use of actual Ukrainian data it was established that the delta-normal technique turned out to be inadequate due to violation of assumption regarding normality of currencies exchange rates. The historical modeling technique provides acceptable results in conditions of stable market situations only. It showed unsatisfactory characteristics of adaptation to varying market factors and cannot be applied for analysis of unstable financial markets. Quite acceptable results of forecasting possible losses were received by making use of Monte Carlo simulation that hypothetically can take into account possible variations of the market exchange rates. It was established that the risk forecasting errors appear only due to non-predictable abrupt changes of exchange rates. However the model of this type is adapting quickly to the changes.