Publicação
Excesses, durations and forecasting value-at-risk
| Resumo: | The first part of this thesis is devoted to the semiparametric estimation of high quantiles. The classic estimators do not enjoy a desirable property in the presence of linear transformation of the data. To solve this problem, the Peaks Over a Random Threshold (PORT) methodology and PORT estimators are proposed. The consistency and asymptotic normality of the estimators are demonstrated. The finite sample behaviour of the proposed PORT estimators is studied and compared with some competitors. Under the context of financial time series and forecasting Value-at-Risk (VaR), the tendency to clustering of violations problem arises. To deal with this, a new class of independence tests for interval forecasts evaluation is proposed and the choice of one test is addressed. The exact and the asymptotic distributions of the corresponding test statistic are derived. In simulation studies, the proposed test revealed to be more powerful than the other tests under study, with few exceptions. The tendency to clustering of violations problem is related with the discrete Weibull distribution, through the shape parameter. A new estimator for this parameter is proposed. The conditional distribution function and the moments are derived. In order to solve the tendency to clustering of violations problem, a new risk model based on durations between excesses over a high threshold (DPOT) is proposed and compared with state-of-the art models under the probability 0.01, established in the Basel Accords. Under the context of extremal quantiles and using one of the oldest financial time series, the DPOT model and a risk model that uses an PORT estimator are compared with other risk models. In the empirical studies presented, to predict the VaR at a level 0.01 or lower, these models revealed more accuracy than the conditional parametric models widely used by the econometricians. |
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| Autores principais: | Santos, Paulo José Araújo dos, 1972- |
| Assunto: | Teoria dos valores extremos Gestão do risco Séries temporais Distribuição de Weibull Teses de doutoramento - 2011 |
| Ano: | 2011 |
| País: | Portugal |
| Tipo de documento: | tese de doutoramento |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| Resumo: | The first part of this thesis is devoted to the semiparametric estimation of high quantiles. The classic estimators do not enjoy a desirable property in the presence of linear transformation of the data. To solve this problem, the Peaks Over a Random Threshold (PORT) methodology and PORT estimators are proposed. The consistency and asymptotic normality of the estimators are demonstrated. The finite sample behaviour of the proposed PORT estimators is studied and compared with some competitors. Under the context of financial time series and forecasting Value-at-Risk (VaR), the tendency to clustering of violations problem arises. To deal with this, a new class of independence tests for interval forecasts evaluation is proposed and the choice of one test is addressed. The exact and the asymptotic distributions of the corresponding test statistic are derived. In simulation studies, the proposed test revealed to be more powerful than the other tests under study, with few exceptions. The tendency to clustering of violations problem is related with the discrete Weibull distribution, through the shape parameter. A new estimator for this parameter is proposed. The conditional distribution function and the moments are derived. In order to solve the tendency to clustering of violations problem, a new risk model based on durations between excesses over a high threshold (DPOT) is proposed and compared with state-of-the art models under the probability 0.01, established in the Basel Accords. Under the context of extremal quantiles and using one of the oldest financial time series, the DPOT model and a risk model that uses an PORT estimator are compared with other risk models. In the empirical studies presented, to predict the VaR at a level 0.01 or lower, these models revealed more accuracy than the conditional parametric models widely used by the econometricians. |
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