Impact of parameter uncertainty on Value-at-Risk estimates when few data is available

In this thesis I investigated the impact of parameter uncertainty on the 99.5 percent one year Value-at-Risk (VaR), in particular the impact of having only a few years of available data. In a simulation study where the underlying data generation process is known, I applied estimation methods that do and do not take into account the effect of parameter uncertainty to show if, and by how much these estimation methods differ from the known VaR. The data generating processes I used vary from a Gaussian copula to a Clayton copula. Within the simulation study I differentiated between the impact of parameter uncertainty on the VaR for the correlation, variances and Clayton copula parameter. Finally, I applied the different estimation methods on the return series used for the Solvency II calibration of the Solvency II Capital Requirement for equity investments. I found that including parameter uncertainty results in a smaller probability of underestimating the true 99.5 percent one year VaR and less economic impact of underestimating the true 99.5 percent one year VaR as compared to VaR estimates obtained using Maximum Likelihood Estimation. Furthermore, incorporating parameter uncertainty, within the context of Solvency II equity module, re- sulted in a more strict Solvency II Capital Requirement.