  The Solvency II Directive and Solvency Assessment and Management (the South
African equivalent) give a Solvency Capital Requirement which is based on a
99.5% Value-at-Risk (VaR) calculation. This calculation involves aggregating
individual risks. When considering log returns of financial instruments,
especially with share prices, there are extreme losses that are observed from
time to time that often do not fit whatever model is proposed for the regular
trading behaviour. The problem of accurately modelling these extreme losses is
addressed, which, in turn, assists with the calculation of tail probabilities
such as the 99.5% VaR. The focus is on the fitting of the Generalized Pareto
Distribution (GPD) beyond a threshold. We show how objective Bayes methods can
improve parameter estimation and the calculation of risk measures. Lastly we
consider the choice of threshold. All aspects are illustrated using share
losses on the Johannesburg Stock Exchange (JSE).
