“…The point-process POT model approximates the time-varying conditional probability of an extreme loss over a given day with the help of a conditional intensity function that characterizes the arrival rate of such extreme events. The intensity function can either be formulated in the spirit of the self-exciting Hawkes process [ 4 , 5 , 10 , 11 , 12 ] (which is extensively used in geophysics and seismology), in the form of the observation-driven autoregressive conditional intensity (ACI) model [ 13 ], or using the autoregressive conditional duration (ACD) models [ 6 , 7 , 8 ] (the last two methodologies were very popular in the area of market microstructure and the modeling of financial ultra-high-frequency data [ 15 , 16 , 17 ]). In all cases, the timing of extreme losses depends on the timing of extreme losses observed in the past.…”