Extreme Value Statistical Theory And Its Applications In Financial Risk Management

Extreme events rarely appear in our daily life, but it will bring tremendous impact once it happens. In recent years people began to focus on extreme events study. Extreme value theory is the model technology to study such events risk with small probability. The theory can predict and assess the risk of extreme events. In this dissertation, the properties of extreme value models, parametric estimations of compound extreme value distribution and their applications in financial risk management fields are studied intensively. The main achievements are listed as follows:1. Poisson-Gumbel compound extreme value distribution is widely used on sea conditions. In this paper, the model variables have been given the financial means and the model is introduced to the area of financial risk management. Maximum likelihood method(MLE), compound moment method (CME)and probability- weighted moment method (PWM)are used to estimate the parameters of the distribution function respectively. Through Monte Carlo simulation, it compares the statistical characters of these methods and draws a conclusion that there is little difference between the results of PWM and MLE. PWM is a good estimation method and it behaves steadily. Finally, it gives an example of foreign exchange rate and shows that the model has a good applicability.2. Combining the principle of generalized Pareto(GP)distribution fitting the tail of a distribution with compound extreme value distribution theory, this paper puts forward Poisson-GP compound threshold distribution model, and gives the results estimated by MLE, CMM and PWM respectively. With the example, Poisson-Gumbel model and Poisson-GP model are analyzed comparatively. The empirical results show that we will choose Poisson-Gumbel model for short time prediction and choose Poisson-GP model for long time prediction.3. The thesis comes up with value at risk (VaR) error model. The parametric error transfer coefficients and elasticity coefficients in Poisson-Gumbel model and Poisson-GP model are studied to compare their fitting efficiency. The conclusions drawn are as follows: from the parametric error transfer coefficient point of view, VaR estimated by Poisson-Gumbel model is more efficient than that estimated by Poisson-GP model; from the parametric elasticity coefficient point of view, there is no significant difference between the two models.4. Portfolio increasingly complex, the original copulas with single parameter have already could not describe the dependent structure among portfolios sufficiently. Symmetrical Bernstein Copula in form of multinomial is one of the copulas with multiple parameters. On the basis of foreign exchange rates example, the paper fits the dependent structure by Symmetrical Bernstein Copula, common Bernstein Copula and copulas with single parameter respectively. When the dependent structure between two exchange rates is fairly symmetric, copulas with single parameter can not fit the dependent well, but Symmetrical Bernstein Copula and common Bernstein Copula do well. At the same time Symmetrical Bernstein Copula is more efficient than common Bernstein Copula.