Measurement and Modelling of Dependencies in Economic Capital

R. A. Shaw, A. D. Smith and G. S. Spivak

British Actuarial Journal, 2011, vol. 16, issue 3, 601-699

Abstract: This paper covers a number of different topics related to the measurement and modelling of dependency within economic capital models. The scope of the paper is relatively wide. We address in some detail the different approaches to modelling dependencies ranging from the more common variance-covariance matrix approach, to the consideration of the use of copulas and the more sophisticated causal models that feature feedback loops and other systems design ideas. There are many data and model uncertainties in modelling dependency and so we have also endeavoured to cover topics such as spurious relationships and wrong-way risk to highlight some of the uncertainties involved. With the advent of the internal model approval process under Solvency II, senior management needs to have a greater understanding of dependency methodology. We have devoted a section of this paper to a discussion of possible different ways to communicate the results of modelling to the board, senior management and other interested parties within an insurance company. We have endeavoured throughout this paper to include as many numerical examples as possible to help in the understanding of the key points, including our discussion of model parameterisation and the communication to an insurance executive of the impact of dependency on economic capital modelling results. The economic capital model can be seen as a combination of two key components: the marginal risk distribution of each risk and the aggregation methodology which combines these into a single aggregate distribution or capital number. This paper is concerned with the aggregation part, the methods and assumptions employed and the issues arising, and not the determination of the marginal risk distributions which is equally of importance and in many cases equally as complex.

Date: 2011
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