Fuzzy Risk Measure for Operational Risk

Abstract

Operational risk is one of the most hazardous types of risk banks face. Banks must take caution and reserve capital to meet these risks. Value at Risk (VaR) and Expected Shortfall (ES) used to measure operational risk and estimate the required capital to meet it. Value at Risk is not sub-additive and measure risk at specific point in risk position, i.e. does not measure the risk in the tail, while Expected Shortfall examines only the left tails of the loss distribution. At the same time, to apply VaR or ES banks must have enough historical data. On the other hand, banks need an early warning indictor to monitor the movement of the capital needed to meet operational risk and take correction action in appropriate time. In this paper we will introduce new risk measure based on fuzzy numbers. The main advantage of the new risk measure is that the banks can use it as an early warning indictor to monitor the capital required to meet risk. At the same time can be used as an alternative to VaR but have more desirable properties. The application of the proposed risk measure shown that, the obtained results are more reliable and accurate at the same time the proposed risk measure have more desirable properties than VaR and ES.