Extreme risks of financial investments

A range of statistical models for the joint distribution of different financial market returns has been developed. The statistical property of interest is the tail behaviour of these models and their abilities to capture features of extreme events in the financial markets, such as sharp falls in one or multiple markets within a short period of time. A conditional approach based on multivariate extreme value theory is considered and compared to a few other benchmark models commonly used in the industry. The conditional approach is extended to have hierarchically structured parameters with the aim to incorporate the underlying financial market factors. Analysis based on both simulated and empirical data shows that the proposed approaches are more suited for modelling the extreme events than the industrial benchmarks