Il Loss Distribution Approach per quantificare i requisiti di capitale per rischi operativi nelle compagnie di assicurazione secondo Solvency II

The new Solvency II regulatory framework is quickly approaching and few researches have been conducted in the insurance sector for what concerns the measurement of operational risk and its respective capital charge. In the near future, in order to calculate the Solvency Capital Requirement (SCR) prescribed by the European Directive, every insurance company will have to choose between using a Standard Formula proposed by the regulator, which is just a percentage of accounting figures, or developing and implementing an Internal Model calibrated in order to reflect better their risk profile. The purpose of my work is to investigate the possibility of using the statistical/actuarial Loss Distribution Approach (LDA) as Internal Model in order to quantify the SCR intended for covering operational risk for a general insurance company. Moreover, the study covers to three insurers of different size in order to understand how the capital charges react to the dimensions of the company. The starting point of the LDA is the Business Line-Event Type (BL-ET) matrix in which the operational losses are collected and arranged. Specifically, 18 BLs and 7 ETs have been considered, yielding 126 combinations. Accordingly, after having calibrated a frequency distribution and a severity distribution for each cell, an aggregate loss distribution is computed by Monte Carlo simulation and through a VaR99.5% risk measure the SCR is found. The result is a matrix of SCRs, one for each BL/ET combination. At this point, the SCR(i,j) have been aggregated under three hypothesis of correlation: zero, partial and full. For what concern the partial correlation analysis, in order to overcome the lack of a real correlation matrix, three cases of uniformly randomly generated correlation coefficients between 0 - 0,50, 0 - 0,75 and 0 - 0,99 have been analyzed. For each range, the matrix has been generated 1.000 times in order to construct a confidence interval. In addition, a sensitivity analysis has been conducted on the convergence of the capital charge by the increasing of the number of simulations and a different risk measure has been tested. Finally a comparison between the results of the Internal Model and the capital charges determined with the Standard Formula has been carried out.