Risk capital reserve and measurement precision in modeling heavy-tailed single operational losses

Jianming Mo and Xiang Gao

Abstract

Heavy and long tails of loss distributions, an extremely high confidence level and parameter-estimation-based measurement techniques can lead to measurement errors in the calculation of capital reserve for extremal risks faced by financial institutions. However, studies on the connectedness between the capital reserve and the measurement uncertainty are surprisingly sparse. This paper attempts to simultaneously quantify single operational losses using a general convolution approach and compute the precision of the quantification output using an error propagation theory. By linking these two models up, the authors find a nonmonotonic and uncertain relationship between the risk capital estimate and its precision, with exact patterns determined by a set of characteristic parameters of the loss distributions chosen. Such patterns are substantiated by the empirical evidence from the literature. This paper provides a rationale for adopting quantitative buffer capital, designed to absorb variations due to measurement errors, especially those originating from the estimation risk.