Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes, a situation rarely encountered in operational risk. We study MLE in operational risk models for small sample-sizes across a range of loss severity distributions. We apply these results to assess (1) the approximation of parameter confidence intervals by asymptotic normality, and (2) value-at-risk (VaR) stability as a function of sample-size. Finally, we discuss implications for operational risk modeling .
Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes, a situation rarely encountered in operational risk. In this paper, we study how asymptotic normality does--or does not--hold for common severity distributions in operational risk models . We then apply these results to evaluate errors caused by failure of asymptotic normality in constructing confidence intervals around the MLE fitted parameters .
R
We study MLE
In this paper, we study how asymptotic normality does--or does not--hold for common severity distributions
R
for small sample-sizes across a range of loss severity distributions. We
. We then
R
assess (1) the approximation of parameter confidence intervals by asymptotic normality, and (2) value-at-risk (VaR) stability as a function of sample-size. Finally, we discuss implications for operational risk modeling
evaluate errors caused by failure of asymptotic normality in constructing confidence intervals around the MLE fitted parameters