Keywords: copulae, two-step estimation, operational risks, value at risk, VaR, expected shortfall, risk measurement, risk assessment, copula distributions
Copulae and operational risks
The motivation of this paper is to develop efficient statistical methods aimed at measuring operational risk. A number of recent legislations and market practices are motivating such developments. For instance, 'the New Basel Capital Accord' (Basel II, 2001), published by Basel Committee on Banking supervision, requires financial institutions to measure operational risks, defined as 'the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events'. The main aim of operational risk models is to set aside an amount of capital that can cover unexpected losses. This is typically achieved estimating a loss distribution deriving functions of interest from it (such as the Value at Risk (VaR)). Statistical models for operational risk estimation face the difficulty that there are a large number of loss distributions to be estimated (in the Basel II framework, at least 56). Current approaches treat these distributions as perfectly dependent, thus overestimating VaR. We propose to use copula distributions to model high dimensional operational risks in a more flexible way, that takes (partial) dependence into account.