Research projects

Project CEMAPRE internal

TitleDynamic Models for Extreme Events
ParticipantsJoão Nicolau (Principal Investigator)
SummaryWe 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