We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot be...

In this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution...

Operational risk management remains a major concern for financial institutions. Indeed, institutions are bound to manage their own funds to hedge this risk. In this paper, we propose an approach to allocate one's own funds based on a combination of historical data and expert opinion using the...

1 Introduction -- 2 Motivation -- Part I MEASURES -- 3 Basic Terms and Notation -- 4 Historical Value-at-Risk -- 5 Sensitivities -- 6 Stress Tests -- 7 Analytical Value-at-Risk -- 8 Expected Shortfall -- 9 Model Choices -- 10 A Monte Carlo Modi cation -- 11 Support Measures -- Part II OPERATIONS...