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This paper 1 proposes a new duration-based backtesting procedure for VaR forecasts. The GMM test framework proposed by Bontemps (2006) to test for the distributional assumption (i:e: the geometric distribution) is applied to the case of the VaR forecasts validity. Using simple J-statistic based on the moments de…ned by the orthonormal polynomials associated with the geometric distribution, this new approach tackles most of the drawbacks usually associated to duration based backtesting procedures. First, its implementation is extremely easy. Second, it allows for a separate test for unconditional coverage, independence and conditional coverage hypothesis (Christo¤ersen, 1998). Third, feasibility of the tests is improved. Fourth, Monte-Carlo simulations show that for realistic sample sizes, our GMM test outperforms traditional duration based test. An empirical application for Nasdaq returns con…rms that using GMM test leads to major consequences for the ex-post evaluation of the risk by regulation authorities. Without any doubt, this paper provides a strong support for the empirical application of duration-based tests for VaR forecasts.

This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is dened as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR dened at an extremely low coverage probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.JEL classication: G21, G28, G32

This study proposes to investigate the threshold effects in the productivity of infrastructure investment in developing countries. It concludes to their presence in the relationship between output and private and public inputs as well as network effects in the productivity of infrastructure. When the available stock of infrastructure is low, investment has the same productivity as non‐infrastructure investment. On the contrary, when a minimum network is available, the marginal productivity of infrastructure investment is greater than the productivity of other investments. Finally, when the main network is achieved, its marginal productivity becomes similar to the productivity of other investment.