## Project CEMAPRE internal

Title | Dynamic Models for Extreme Events |

Participants | João Nicolau (Principal Investigator) |

Summary | We want to investigate a new model that takes into account the dynamic dependencies of block maxima M_{t}. The model relates the current behavior of M_{t} to the its past value, through a conditional distribution that converges to the Generalized Extreme Value Distribution (GEV), as required by the Extreme Value Theory. This model is useful when the sequence of block maxima displays temporal dependency, either because the block size is small or simply because there is too much dependency in the data. The block length trade-off (large blocks generate few observation and high variance versus small blocks violating the asymptotic support for the model, leading to bias) turns out to be less relevant with our approach. In the presence of temporal dependency, the model can be used to obtain density forecasts given the current state or block maximum, that ultimately converge to the GEV distribution, as the forecast horizon increases. Hence, the model allows to perform dynamic risk management, i.e. to evaluate certain extreme financial risks given current market background. Some of these aspects are illustrated with an empirical application to the Dow Jones stock exchange index. |