Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/195412 
Year of Publication: 
2017
Citation: 
[Journal:] Revista de Métodos Cuantitativos para la Economía y la Empresa [ISSN:] 1886-516X [Volume:] 23 [Publisher:] Universidad Pablo de Olavide [Place:] Sevilla [Year:] 2017 [Pages:] 48-74
Publisher: 
Universidad Pablo de Olavide, Sevilla
Abstract: 
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.
Subjects: 
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
JEL: 
C22
C58
G32
Creative Commons License: 
cc-by-sa Logo
Document Type: 
Article

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