Value-at-Risk testing: intraday risk measures and validation tests.

Summary This thesis contributes to the literature on the two main research axes related to Value-at-Risk (VaR): forecasting and backtesting of VaR. Concerning the first axis, the thesis develops a methodology for forecasting VaR at intraday horizons. The methodology conditions non-linearly the returns on the existence of news on the market, measured by the innovation of the transactional intensity. To this end, we introduce two new specifications: a volatility model that links the asymmetric response of volatility to returns to the existence of news and a regime-switching model in the tail of the distribution driven by the existence of news. Empirical applications demonstrate that this methodology is a flexible risk management tool in markets with increasingly large intraday price fluctuations. For the second axis, we introduce two new approaches for VaR backtesting. First, we develop a test that extends the existing ones by checking the validity of VaR for several confidence levels. The test statistic is an extension to the multivariate framework of the Ljung-Box test for the VaR violation process. Second, we use the (geometric) distribution of the duration between two consecutive violations under the assumption of VaR validity and introduce a new test statistic, derived from the moment conditions induced by the orthonormal polynomials associated with the geometric distribution. It is shown that both new tests have good properties at finite distance.