Extreme Value Theory: An Application to the Peruvian Stock Market Returns // Teoría de valores extremos: una aplicación a los retornos bursátiles peruanos

Autores/as

  • Gabriel Rodríguez Pontificia Universidad Católica del Perú

Palabras clave:

extreme value theory, value-at-risk (VaR), expected short-fall (ES), generalized Pareto distribution (GPD), Gumbel distribution, exponential distribution, Fréchet distribution, extreme loss, Peruvian stock market

Resumen

Using daily observations of the index and stock market returns for the Peruvian case from January 3, 1990 to May 31, 2013, this paper models the distribution of daily loss probability, estimates maximum quantiles and tail probabilities of this distribution, and models the extremes through a maximum threshold. This is used to obtain the better measurements of the Value at Risk (VaR) and the Expected Short-Fall (ES) at 95% and 99%. One of the results on calculating the maximum annual block of the negative stock market returns is the observation that the largest negative stock market return (daily) is 12.44% in 2011. The shape parameter is equal to -0.020 and 0.268 for the annual and quarterly block, respectively. Then, in the first case we have that the non-degenerate distribution function is Gumbel-type. In the other case, we have a thick-tailed distribution (Fréchet). Estimated values of the VaR and the ES are higher using the Generalized Pareto Distribution (GPD) in comparison with the Normal distribution and the differences at 99.0% are notable. Finally, the non-parametric estimation of the Hill tail-index and the quantile for negative stock market returns shows quite instability.

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Usando observaciones diarias del índice y los retornos bursátiles para el caso Peruano desde el 3 de enero de 1990 hasta el 31 de mayo de 2013, este documento modela la distribución de las probabilidades de pérdidas diarias, estima los cuantiles máximos y las colas de la distribución y finalmente, modela los valores extremos usando un umbral máximo. Todo esto es usado para obtener una mejor medida del valor en riesgo (VaR) y de la pérdida esperada (ES) al 95% y 99% de confianza. Uno de los resultados de calcular el bloque máximo anual de los retornos bursátiles negativos es la observación que el retorno bursátil más negativo (diario) es 12.44% en el 2011. El parámetro de forma es igual a -0.020 y 0.268 para los bloques anuales y trimestrales, respectivamente. En consecuencia en el primer caso tenemos una distribución de tipo Gumbel. En el otro caso se tiene una distribución de cola pesada (Fréchet). Los valores estimados para el VaR y el ES son más elevados utilizando una distribución de tipo Pareto Generalizada (GPD) en comparación con la distribución normal y las diferencias al 99% son remarcables. Finalmente, la estimación no paramétrica del indice de cola de Hill y del cuantil para retornos negativos muestra ser bastante inestable.

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Publicado

2017-07-01

Cómo citar

Rodríguez, G. (2017). Extreme Value Theory: An Application to the Peruvian Stock Market Returns // Teoría de valores extremos: una aplicación a los retornos bursátiles peruanos. Revista De Métodos Cuantitativos Para La Economía Y La Empresa, 23, Páginas 48 a 74. Recuperado a partir de https://www.upo.es/revistas/index.php/RevMetCuant/article/view/2686

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