I. An empirical examination of extreme value theory methods in VaR estimation. II. Extreme value theory and the pricing of catastrophe derivatives. III. Measuring change in tail behavior with an application to emerging financial markets in Asia

I. In this paper, we examine various issues in applying Extreme Value Theory (EVT) methods to estimate Value-at-Risk (VaR) of financial data. Empirical comparisons of EVT and existing methods are made using daily exchange rate series. We find that while EVT methods provide a powerful alternative way of estimating unconditional tail distribution, they do not offer clear advantage over existing methodology at non-extreme tails such as 95%. Their superiority in performance is more pronounced as one goes further into the tails. Empirical issues with regard to the application of EVT models to financial data are examined using Monte Carlo simulations. Several VaR model comparison rules are also studied and our results show that one needs to be cautious when applying the “pre-commitment approach” to select VaR models.; II. This paper examines the pricing methodology on a new asset class whose payoffs are linked to losses from natural disasters. These assets potentially could be very attractive to investors because they have low correlations with stock market and interest rate movements. The pricing of these instruments, however, presents new challenge because of the difficulties in pricing the insurance feature of the products, most notably tail estimation. In this paper, we explore using extreme value theory (EVT) methods to price these innovative products. Our method differs from existing ones in that it models tail only. Empirical analysis is provided using PCS option data.; III. This paper explores tests of the hypothesis that the tail thickness of a distribution is constant over time. Using Hill's conditional maximum likelihood estimator for the tail index of a distribution, tests of tail shape constancy are constructed that allow for an unknown breakpoint. The recursive test is shown to be inconsistent in one direction, and only a one-sided test is recommended. Specifically, the test can be used when the alternative hypothesis is that the tail index decreases over time. A rolling and sequential version of the test is consistent in both directions. The methods are illustrated on recent stock price data for Thailand, Malaysia and Indonesia. The period covers the recent Asian financial crisis and enables us to assess whether breakpoints in domestic asset return distributions are related to known changes in institutional in the foreign currency markets of these countries.