Extreme value theory with Markov chain Monte Carlo - an automated process for EVT in finance

Abstract: The purpose of this thesis was to create an automated procedure for estimating financial risk using extreme value theory (EVT). The "peaks over threshold" (POT) result from EVT was chosen for modelling the tails of the distribution of financial returns. The main difficulty with POT is choosing a convergence threshold above which the data points are regarded as extreme events and modelled using a limit distribution. It was investigated how risk measures are affected by variations in this threshold and it was deemed that fixed-threshold models are inadequate in the context of few relevant data points, as is often the case in EVT applications. A model for automatic threshold weighting was proposed and shows promise. Moreover, the choice of Bayesian vs frequentist inference, with focus on Markov chain Monte Carlo (MCMC) vs maximum likelihood estimation (MLE), was investigated with regards to EVT applications, favoring Bayesian inference and MCMC. Two MCMC algorithms, independence Metropolis (IM) and automated factor slice sampler (AFSS), were analyzed and improved in order to increase performance of the final procedure. Lastly, the effects of a reference prior and a prior based on expert opinion were compared and exemplified for practical applications in finance.