Abstract
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 analytically determined in advance. Usually, the frequency and the severity distributions should be adequately combined and elaborated with Monte Carlo methods, in order to estimate the loss distributions and risk measures. Naturally, financial analysts and regulators are interested in mitigating sampling errors, as prescribed in EU Regulation 2018/959. In particular, the sampling error of the 99.9% quantile is of paramount importance, along the lines of EU Regulation 575/2013. The Monte Carlo error for the operational risk measure is here assessed on the basis of the binomial distribution. Our approach is then applied to realistic simulated data, yielding a comparable precision of the estimate with a much lower computational effort, when compared to bootstrap, Monte Carlo repetition, and two other methods based on numerical optimization.
Highlights
International financial institutions typically calculate capital requirements for operational risk via the advanced measurement approach (AMA)
The AMA is based on statistical models that are internally defined by institutions and comply with regulatory requirements
The loss data is categorized by Operational Risk Categories (ORCs), such that the independent and identical distribution hypothesis is applicable within each ORC
Summary
International financial institutions typically calculate capital requirements for operational risk via the advanced measurement approach (AMA). 99.9% quantile of the overall annual loss distribution as the sum between the expected loss and the unexpected loss, from which the expected loss could be eventually deducted To obtain this deduction, it is necessary to comply with the requirements reported in European Parliament and Council of the European Union (2018): the expected loss estimation process is done by ORC and is consistent over time; the expected loss is calculated using statistics that are less influenced by extreme losses, including median and trimmed mean, especially in the case of medium- or heavy-tailed data; the maximum offset for expected loss applied by the institution is bounded by the total expected loss; the maximum offset for expected loss in each ORC is bound by the relevant expected losses calculated according to the institution’s operational risk measurement system applied to that category; the offsets the institution allows for expected loss in each ORC are capital substitutes or available to cover expected loss with a high degree of certainty (e.g., provisions) over the one-year period; specific reserves for exceptional operational risk loss events, that have already occurred, cannot be used as expected loss offsets.
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