Aims - This module aims to develop a core mathematical and statistical understanding of an important new emerging area of risk modelling known as Operational Risk which arose from the development of the Basel II/III banking regulatory accords. This will equip students with the necessary tools to undertake core modelling activities required in risk management, capital management and quantitative modelling in modern financial institutions. It is primarily intended for third and fourth year undergraduate students and taught postgraduate students registered on the degree programmes offered by the Department of Statistical Science, or jointly with other departments.

Objectives - On successful completion of the module, a student should be able to: describe the key quantitative requirements of the Basel II/III banking accord; describe the 56 risk cells (business units and risk types) required under the standard Basel II/III regulator frameworks; describe the basic indicator, standardized and advanced measurement approaches; describe the key components of a loss distributional approach model; develop frequency and heavy tailed severity models for Operational risk types including estimation or the model parameters and model selection; describe properties and asymptotic estimators for risk measures that are required for capital calcultion; describe the coherent allocation of capital to business units from the institutional level; introduce and understand the influence of dependence modelling within an LDA model structure; obtain familiarity with particular classes of copula statistical models of basic relevance to practical Operational risk modelling; decide upon appropriate combining approaches for different sources of data required by regulation to be considered in OpRisk settings; develop loss aggregation methods to aggregate OpRisk loss processes.

Applications - An integral part of modern financial risk involves Operational Risk, the third key risk type that financial institutions must model and hold capital for according to the international banking regulations of Basel II/III. The key set of concepts and mathematical modelling tools developed in this module will equip the future risk modellers and quantitative analysts with the appropriate core mathematical and statistical background to undertake development of such risk models in industry.

Content - Key components of operational risk frameworks, external databases, scenario analysis, operational risk in different financial sectors, risk organization and governance. Basic indicator approach, standardized approaches, advanced measurement approach. Loss distributional approach: quantiles and moments, frequency distributions, severity distributions and heavy tailed models, convolutions and characteristic functions, basic asymptotics of compound processes, modelling truncated and censored data constant threshold Poisson process, negative binomial and binomial processes, effects of ignoring data truncation, time varying thresholds, stochastic unobserved thresholds. Measures of risk: coherent and convex risk measures, comonotonic additive risk measures, value-at-risk, expected shortfall, spectral risk measures, distortion risk measures, risk measures and parameter uncertainty. Capital Allocation: coherent capital allocation, Euler allocation, allocation of marginal contributions, estimation of risk measures and numerical approximations. Modelling dependence: dependence modelling in the LDA framework, dependence between frequencies, dependence between severities, dependence between annual losses, common factor models, copula modelling. Combining different data sources: internal, external and expert opinions, Bayesian methods, minimum variance, credibility methods. Loss aggregation: calculation of the annual loss distribution, calculation of the institution wide annual loss.

Key texts - Available from ReadingLists@UCL.