Extreme Value Statistics and Quantile Estimation with Applications in Finance and Insurance

Doctoral thesis, 2007

This thesis presents results in Extreme Value Statistics and quantile estimation. A first part includes a popular scientific introduction to Extreme Value Statistics and a review paper on Extreme Value Theory in finance. Further, we study new non-parametric quantile estimators for non-extreme quantiles. After concluding that these have the same asymptotic distribution as sample quantiles, a simulation study shows that their small sample performance is better in many cases than that of the sample quantile. In the part of this thesis dealing with finance we study extreme dependence between stock market log returns sampled at different frequencies using the so-called tail dependence function. We also investigate the "stylized fact" that log returns have Semi-heavy tails. The next topic is insurance losses resulting from wind storm damages in southern Sweden. A detailed statistical analysis detects a weak trend, that non-extreme quantiles of individual storms increase with time, but no other trends. We also find prediction intervals for the sizes of future storm losses using both a univariate and a bivariate model. One conclusion is that the major Swedish storm Gudrun was not unlikely to occur. Finally, we introduce the models used in the insurance application into risk management in finance.