Modeling maxima with a regime-switching Fréchet model

Identifying the behavior of extreme values in financial series is known to be complicated by the changing returns in different periods. To address this, we construct a novel and simple conditional generalized extreme value (GEV) framework exploiting a Markov-switching mechanism to model the time-varying behavior of maxima series. Our proposed regime-switching Fréchet (RSF) model considers the shape parameter and the scale parameter to be time-varying, and model estimation is performed by maximum likelihood. Simulations validate the flexibility of the RSF model in finite samples. In empirical applications, we analyze two real data examples, the Dow Jones Industrial Average index and the SSE50 index of the Shanghai Stock Exchange, illustrating that our method captures the dynamics and transitions of the tail well. There is an apparent inverse relationship between the maxima and the tail index. The RSF model is more accurate than the static GEV model. An out-of-sample conditional value-at-risk forecast analysis confirms the merits of the RSF approach.