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Subject: search.filters.subject.Extreme value theory

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    Assessing tail-related risk for heteroscedastic return series of Asian emerging equity markets : a thesis presented in partial fulfillment of the requirements for Master of Business Studies at Massey University
    (Massey University, 2003) Xu, Qing
    High degrees of leptokurtosis, heteroscedasticity and asymmetries in return series are the common features of Asian emerging equity markets, especially during the financial crisis. Thus, strengthening risk management with improved risk measures becomes increasingly important. According to the Basle Committee on Banking Supervision, the value at risk (VaR) should be calculated at the 99% confidence level or above with daily data. In the context of Asian equity markets, the use of the estimated conditional variance of market returns as the sole measure of market risk may result in serious underestimation of the true risk caused by tail events. Therefore, this research focuses on the tail-related risk measure of nine Asian index returns within the framework of extreme value theory. It employs the generalized extreme value (GEV) and the generalized Pareto distribution (GPD) approaches combined with AR(l)-GARCH(m, s) filtering of the return data. The VaR performances under different distributions with different volatility filtering are compared, and the estimated conditional and unconditional expected shortfalls based on the GPD are reported. The important findings include the following. (1) The nine heteroscedastic index returns indeed follow heavy-tailed distributions rather than the normal distribution. (2) Both the GPD and GEV distributions of daily returns are asymmetric between local maxima (right tail) and local minima (left tail). (3) The results of the GEV approach are somewhat sensitive to the block length chosen, while the GPD approach, with the thresholds determined much less arbitrarily, can avoid equivocalness with the GEV method. (4) The reported results indicate that the VaR based on the extreme value theory at high quantiles (above 99%) is more accurate than the VaR based on the normal distribution.
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    Risk management and extreme scenario development using multiple regime switching approaches : a thesis presented in partial fulfilment of the requirements for the degree of Master of Business Studies in Finance at Massey University
    (Massey University, 2004) Pallem, Dinesh
    Over the last twenty-five years, there have been an increasingly large number of extreme events in the financial markets. This includes market crashes and natural disasters that have led to extremely large losses and claims. Extreme event risk affects all aspects of risk assessment modeling and management. Traditional risk measurement methods focus on probability of laws governing average of sums, and do not focus on the tails of distribution. The investigation concerns the characterization and development of extreme markets scenarios for use in risk measurement and capital adequacy determination frameworks. The first part of the investigation concerns the development of event timelines that can be used for characterizing whether a period of time should be considered normal or extreme market conditions or regimes. The time lines have allowed the identification of the different times when the markets were calm and when the markets were turbulent. They assist in building scenarios, and also to identify the scenarios for decomposition of data to model the different regions, either the tail or the center of the distribution using the mentioned regime switching models. The information from the event time line can be used to define scenarios in a stress testing context. In this investigation, extreme value analysis, which is an extension of the standard VaR techniques, useful in measuring extreme events has been used, which fits density functions by placing more weights in the tails than the normal Gaussian distribution and model the upper and lower tail of an underlying distribution. Extreme value distribution functions including "fat tailed" will be fitted to the tails of critical market factors to model the extreme market events that are not given appropriate probability of occurrence under normal conditions. The Hill estimator, which is recognized as the consistent estimator for empirical analysis is used for calculating the tail index parameter for EVT modeling, However, it has to be noted that the Hill estimator is efficient when the underlying distribution is fat-tailed as compared to the gaussian, where the tail index estimates tend to go to infinity. The performance of Extreme value theory estimation technique with multiple regimes on real and simulated financial time series for efficient results, compared to the standard VaR techniques has been studied. In this investigation, multiple regime switching approach has been used to identify regimes and measure risk accordingly. It is assumed that the center of the returns distribution is normally distributed with 90 percent of the data in the in the center region and each tail contains 5 percent of the data. Three regime switching models have been used in this analysis which includes, the Unconditional LT-C-RT (Left tail - Center - Right Tail) transfers, the 3 State Regime Markov Transition Model and the Geometric Time in Trail Model. The regime switching models are modeled using the following procedures: 1) The Unconditional LT-C-RT (Left Tail - Center - Right Tail) model is an IID model (Independent and Identically Distributed) model and has a simple Bernoulli approach where the market is in a normal state with probability P or an abnormal state with probability 1 - p . The transition between states is independent of the last state. 2) A Markov chain approach where the next state of the market is a function of the current state. That there are the following transitions possible: 2.1) Normal to normal 2.2) Normal to abnormal 2.3) Abnormal to abnormal 2.4) Abnormal to normal 3). The Geometric Time in Tail model is a hybrid Bernoulli approach where the markets stays in a given state based on a duration model and when the duration in a given states has expired, the sampling of the next state using a independent Bernoulli approach similar to approach one. This implies that the after the market has stayed in a given regime for the sample duration time, it can stay in the current regime with probability p or leave the regime with probability 1 - p. The sample duration can be based on the exponential distribution for continuous time and the geometric distribution for discrete time such as daily movements. Tail index estimation results using EVT indicate the presence of fat tails in equity data and the results of Value-at-Risk (VaR) and Expected Shortfall (ES) are considerably similar for the three regime switching models. The comparison of results from the multiple regime switching models to the one region distribution results, which serve as the base case prove the efficiency of using this approach for a better risk measure.