An ensemble of cosmological models based on generalized BFtheory is constructed where the rôle of vacuum (zero-level) coupling constants is played by topologically invariant rational intersection forms (cosmological-constant matrices) of 4-dimensional plumbed Vcobordisms which are interpreted as Euclidean spacetime regions. For these regions describing topology changes, the rational and integer intersection matrices are calculated. A relation is found between the hierarchy of certain elements of these matrices and the hierarchy of coupling constants of the universal (low-energy) interactions.

ResumenEl objetivo de esta investigación es describir y comparar la estimación del Valor en Riesgo (VaR), considerando un modelo GARCH univariado con la innovación de la distribución α-estable. Los resultados estadísticos sugieren que el modelo VaR α-estable proporciona estimaciones del VaR más precisas que el modelo bajo la hipótesis gaussiana, el cual subestima significativamente el VaR en períodos de alta volatilidad. Por el contrario, en el período posterior a la crisis, el VaR al 95% bajo la hipótesis gaussiana muestra resultados aceptables y el obtenido bajo el modelo α-estable se encuentra por debajo del rango admisible. La principal aportación de esta investigación es que propone una distribución condicional alternativa para los rendimientos de los precios de los activos en el mercado financiero mexicano, considerando un modelo GARCH con la innovación de la distribución α-estable. Porúltimo, esta investigación proporciona evidencia de que el modelo VaR α-estable estima satisfactoriamente el VaR para niveles altos de confianza incluso en períodos de alta volatilidad. En contraste, en períodos de relativa tranquilidad para niveles de confianza bajos este modelo sobrestima las pérdidas potenciales. is below the admissible range. The main contribution of this research is that it proposes an alternative conditional distribution for asset price yields in the Mexican financial market, considering a GARCH model with the innovation of the α-stable distribution. Finally, this research provides evidence that the α-stable VaR model satisfactorily estimates the VaR for high levels of confidence even in periods of high volatility. In contrast, in periods of relative financial tranquility for low confidence levels, this model overestimates potential losses.JEL Classification: G17, C22, C13.

PurposeThis paper tests the accuracies of the models that predict the Value-at-Risk (VaR) for the Market Integrated Latin America (MILA) and Association of Southeast Asian Nations (ASEAN) emerging stock markets during crisis periods.Design/methodology/approachMany VaR estimation models have been presented in the literature. In this paper, the VaR is estimated using the Generalized Autoregressive Conditional Heteroskedasticity, EGARCH and GJR-GARCH models under normal, skewed-normal, Student-t and skewed-Student-t distributional assumptions and compared with the predictive performance of the Conditional Autoregressive Value-at-Risk (CaViaR) considering the four alternative specifications proposed by Engle and Manganelli (2004).FindingsThe results support the robustness of the CaViaR model in out-sample VaR forecasting for the MILA and ASEAN-5 emerging stock markets in crisis periods. This evidence is based on the results of the backtesting approach that analyzed the predictive performance of the models according to their accuracy.Originality/valueAn important issue in market risk is the inaccurate estimation of risk since different VaR models lead to different risk measures, which means that there is not yet an accepted method for all situations and markets. In particular, quantifying and forecasting the risk for the MILA and ASEAN-5 stock markets is crucial for evaluating global market risk since the MILA is the biggest stock exchange in Latin America and the ASEAN region accounted for 11% of the total global foreign direct investment inflows in 2014. Furthermore, according to the Asian Development Bank, this region is projected to average 7% annual growth by 2025.

<p>En el sector petrolero, el VaR se ha implementado con el objetivo de cuantificar lo mejor posible los movimientos extremos de los precios del petróleo, debido a que estos repercuten la actividad económica y afectan significativamente los movimientos en el mercado accionario (Sadorsky, 1999). Con este propósito, en esta investigación cuantificamos el VaR considerando tres tipos de petróleo (Brent, WTI y MME) y analizamos el desempeño de la estimación del VaR a un día mediante el estadístico de Kupiec considerando modelos GARCH con tres distribuciones alternativas en el proceso de innovación: estable, t-Student generalizada asimétrica y normal en un período de alta volatilidad. Los resultados de la evaluación de desempeño del modelo basado en el estadístico de Kupiec señalan que el modelo VaR-estable es un modelo más robusto y preciso para ambos niveles de confianza que los basados en las distribuciónes t-Student generalizada asimétrica y normal.  Este resultado es crucial en el sector financiero, debido a que impacta directamente en la previsión de reservas necesarias para afrontar potenciales pérdidas. <strong></strong></p>

Objective: The purpose of this paper is to explore different distributions in conditional Value at Risk (VaR) modeling as an option in the Mexican market. Methodology: We estimate a GARCH model under the Gaussian, Normal Inverse Gaussian, Skew Generalized t and the Stable distribution assumption, then we implement the model in predicting one-day ahead VaR, and finally we examine the performance among the four VaR models during a period of high volatility. Results: The backtesting result confirms that the stable-VaR approach outperforms the other models in the VaR's prediction at a 99% confidence level. Limitations: Although the VaR is a widely used risk measure, it is not a coherent risk measure, for this reason, a natural extension of our work should be to estimate the expected shortfall and this may produce different insights. Conclusions: Our findings reveal that models that consider some empirical characteristics of financial returns such as leptokurtic, volatility clustering and asymmetry improve the VaR predicting capacity. This finding is important in the search for more robust approaches for VaR estimates.