Risk aggregation and capital allocation using copulas
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Banking is a risk and return business; in order to obtain the desired returns, banks are required to take on risks. Following the demise of Lehman Brothers in September 2008, the Basel III Accord proposed considerable increases in capital charges for banks. Whilst this ensures greater economic stability, banks now face an increasing risk of becoming capital inefficient. Furthermore, capital analysts are not only required to estimate capital requirements for individual business lines, but also for the organization as a whole. Copulas are a popular technique to model joint multi-dimensional problems, as they can be applied as a mechanism that models relationships among multivariate distributions. Firstly, a review of the Basel Capital Accord will be provided. Secondly, well known risk measures as proposed under the Basel Accord will be investigated. The penultimate chapter is dedicated to the theory of copulas as well as other measures of dependence. The final chapter presents a practical illustration of how business line losses can be simulated by using the Gaussian, Cauchy, Student t and Clayton copulas in order to determine capital requirements using 95% VaR, 99% VaR, 95% ETL, 99% ETL and StressVaR. The resultant capital estimates will always be a function of the choice of copula, the choice of risk measure and the correlation inputs into the copula calibration algorithm. The choice of copula, the choice of risk measure and the conservativeness of correlation inputs will be determined by the organization’s risk appetite.