VALUE AT RISK A COMPARISON OF METHODS TO CHOOSE THE SAMPLE FRACTION IN TAIL INDEX ESTIMATION OF GENERALIZED EXTREME VALUE DISTRIBUTION / VALOR EM RISCO UMA COMPARAÇÃO ENTRE MÉTODOS DE ESCOLHA DA FRAÇÃO AMOSTRAL NA ESTIMAÇÃO DO ÍNDICE DE CAUDA DE DISTRIBUIÇÕES GEV

AUTOR(ES)
DATA DE PUBLICAÇÃO

2002

RESUMO

Value at Risk -VaR- is already part of the toolkit of financial analysts assessing market risk. In order to implement VaR it is needed to estimate low quantiles of the portfolio returns distribution. Traditional methodologies combine a normal conditional distribution together with ARCH type models to accomplish this goal. Albeit well succeed in evaluating risk for typical periods, this methodology has not been able to accommodate events that occur with very low probabilities. For these situations one needs conditional distributions with excess of kurtosis. The use of distributions derived from the Extreme Value Theory -EVT-, collectively known as Generalized Extreme Value distribution -GEV-, together with ARCH type models have made it possible to address this problem in a proper framework. A key parameter in the GEV distribution is the tail index, which can be estimated by Hill`s estimator. Hill`s estimator is very sensible, in terms of bias and RMSE, to the sample fraction that is used in its estimation. The objective of this dissertation is to compare three recently suggested methods presented in the statistical literature: the double bootstrap method Danielsson, de Haan, Peng and de Vries 1999,the threshold method Guillou and Hall 2001 and the alternative Hill plot Drees, de Haan and Resnick 2000. The methods have been evaluated with respect to the conditional coverage test of Christoffersen 1998, which has been applied to the following returns series : NASDAQ, NIKKEY, MERVAL e IBOVESPA. Our empirical findings suggests that, overall the three methods have the same performance, with some advantage of the bootstrap and threshold methods over the alternative Hill plot, which has a normative component in the determination of the optimal tail index.

ASSUNTO(S)

value at risk hill estimator distribuicoes gev tail index valor em risco estimador de hill distributions gev indice de cauda

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