The Contagion Box: Measuring Co-movements in Financial Markets by Regression Quantiles∗

We propose a simple new semi-parametric approach to investigate whether co-dependence across markets increase in periods of extreme negative or extreme positive returns relative to quiet periods. Our empirical investigation is based on the computation of a conditional probability: given that returns on a certain market have fallen in the extreme negative or positive tail of their own distribution, we com-pute the probability that returns on a different market will also take on extreme values. Technically, we estimate the probability that re-turns on one market are lower than a given quantile, when returns on another market are also lower than the correspondent quantile. Quan-tiles, which are Þrst kept constant, are next made time-varying us-ing the CAViaR model developed by Engle and Manganelli (2004). Graphically, conditional probabilities can be represented in what we call the contagion box, which is a square with unit side. Loosely speaking, since a 45 line represents the case of independence between two markets, when the conditional probability lies above this line, this indicates presence of co-movements. From this insight rigorous econo-metric tests of contagion are derived and implemented. An application to the so-called tequila crisis is Þnally carried out