Integrating Op Risk into Total VaR
Niklas Wagner and Thomas Wenger
Operational risk (OpR) is the risk of losses at financial institutions due to the failure of internal processes, such as fraud, information technology failures, and lawsuits. The measurement of such risks poses several challenges in its own right: the scarcity of data and the skewness and kurtosis of typical loss distributions. In this chapter we focus on challenges and problems arising in the task of integrating a measure for OpR into an institution’s total value at risk (VaR), along with measures for other risks such as market risk and credit risk. It turns out that many of the aspects that make the measurement of OpR difficult on a stand-alone basis also leave a trace in integrated risk measurement. We provide an approximation method for total VaR based on the Cornish-Fisher expansion. The proposed method of simulated higher moments (MSHM) approach continues to perform reasonably well in cases when the quality of the commonly used variance-covariance method deteriorates. In stylized examples, we also address the question of whether the diversification effect between risks can be expected to hold in the presence of OpR losses.
To clarify the nature of the challenge in calculating an integrated VaR of a portfolio of loss variables X1, . . . , XN, let us take as a starting point the square root (or variance-covariance) formula and consider the levels of knowledge with ...