BIS Working Papers are written by members of the Monetary and Economic Department of the Bank for International Settlements, and from time to time by other economists, and are published by the Bank. The papers are on subjects of topical interest and are technical in character. The views expressed in them are those of their authors and not necessarily the views of the BIS. This publication is available on the BIS website (www.bis.org).

In this study we construct volatility spillover indexes for some of the major stock market indexes in the world. We use a DCC-GARCH framework for modelling the multivariate relationships of volatility among markets. Extending the framework of Diebold and Yilmaz [2012] we compute spillover indexes directly from the series of returns considering the time-variant structure of their covariance matrices. Our spillover indexes use daily stock market data of Australia, Canada, China, Germany, Japan, the United Kingdom, and the United States, for the period January 2001 to August 2016. We obtain several relevant results. First, total spillovers exhibit substantial time-series variation, being higher in moments of market turbulence. Second, the net position of each country (transmitter or receiver) does not change during the sample period. However, their intensities exhibit important time-variation. Finally, transmission originates in the most developed markets, as expected. Of special relevance, even though the Chinese stock market has grown importantly over time, it is still a net receiver of volatility spillovers.

Extreme weather events, like a strong El Niño (ENSO), affect society in many different ways especially in the context of recent globe warming. In the Colombian case, ENSO had a significant impact on consumer food prices during the strongest event in 2015. Our research evaluates the relationship between ENSO and Colombian food inflation growth by using a smooth transition nonlinear model. We estimate the impacts of a strong ENSO on food inflation growth by adopting generalised impulse response functions (GIRFs). The results suggest that the weather shocks are transitory and asymmetric on inflation. A strong El Niño shock has a significant effect on the food inflation growth from five to nine months after the shock, and the accumulated elasticity is close to 730 basic points. We build the GIRFs for eight different episodes associated with a strong El Niño in the period corresponding from March 1962 to December 2018, and there is no evidence of changes in the size of Colombian food inflation growth responses over time. Finally, the negative shock, associated with a strong La Niña, shows an ambiguous effect on food prices.

We study exchange rate dependencies between seven countries from four different regions of the world. Our sample includes two developed countries, the United Kingdom and Germany (representing the Euro Area), two large emerging Asian economies, South Korea and Indonesia, two Latin American countries, Brazil and Chile, and South Africa. The currencies of all of these countries are actively traded in global forex markets and all of them are important for large international portfolio composition and rebalancing. We construct multivariate copula functions using a regular vine copula approach, allowing for very flexible dependency structures. We find evidence of exchange rate contagion for our set of countries. However, important asymmetries are worth noting. First, contagion occurs only during periods of exchange rate appreciation of the different currencies with respect to the United States Dollar. We do not find evidence of contagion for any pair of exchange rates during periods of currency depreciations. Second, contagion is more frequent in pairs of countries that include either the United Kingdom or Germany. In fact, the largest tail dependence coefficient corresponds to the pair composed by these two countries' exchange rates. Third, contagion occurs more within countries of a same region, for instance, between Brazil and Chile, and between Korea and Indonesia. This result shows that, in episodes of large currency appreciation, hedging strategies for global investors taking positions in large markets require regional diversification.

RESUMEN. Este documento realiza una descripción de las medidas de dependencia con sus principales ventajas y desventajas y presenta a la cópula como una estructura flexible que permite caracterizar diferentes tipos de dependencia. Adicionalmente, introduce el uso de la cópula en la medición de riesgo financiero, tomando como ejemplo un portafolio compuesto por tres activos representativos del mercado colombiano.Las pruebas de desempeño o de backtesting del valor en riesgo calculado por diferentes metodologías en los años 2006 y 2007 muestran que las mejores son aquellas que modelan la dependencia en media y varianza, tales como modelos VAR-GARCH-Cópula(t) y VAR-GARCH-Cópula(normal). Las técnicas con el peor desempeño son Riskmetrics R y la basada en el supuesto de normalidad.Palabras Clave. Dependencia, cópula, riesgo de mercado, riesgo de crédito, métodos de simulación de Monte Carlo. Clasificación JEL. C32, C52, G10.Esta versión: 14 de febrero de 2008. Los resultados y opiniones son responsabilidad exclusiva de los autores y su contenido no compromete al Banco de la República ni a su junta directiva. 4 La demostración completa del teorema de Sklar se encuentra en Nelsen [2006]