Looking at Extremes without Going to Extremes: A New Self-Exciting Probability Model for Extreme Losses in Financial Markets

Forecasting market risk lies at the core of modern empirical finance. We propose a new self-exciting probability peaks-over-threshold (SEP-POT) model for forecasting the extreme loss probability and the value at risk. The model draws from the point-process approach to the POT methodology but is built under a discrete-time framework. Thus, time is treated as an integer value and the days of extreme loss could occur upon a sequence of indivisible time units. The SEP-POT model can capture the self-exciting nature of extreme event arrival, and hence, the strong clustering of large drops in financial prices. The triggering effect of recent events on the probability of extreme losses is specified using a discrete weighting function based on the at-zero-truncated Negative Binomial (NegBin) distribution. The serial correlation in the magnitudes of extreme losses is also taken into consideration using the generalized Pareto distribution enriched with the time-varying scale parameter. In this way, recent events affect the size of extreme losses more than distant events. The accuracy of SEP-POT value at risk (VaR) forecasts is backtested on seven stock indexes and three currency pairs and is compared with existing well-recognized methods. The results remain in favor of our model, showing that it constitutes a real alternative for forecasting extreme quantiles of financial returns.