Extremal index estimation: application to financial data

Abstract

In finance it is crucial to understand the risk of occurrence of extreme events such as currency crises or stock market crashes. It is important to model the distribution of extreme events. Extreme value theory is known to accurately estimate quantiles and tail probabilities of financial asset returns. These kinds of data are usual related to heavy tailed distributions, where a relevant parameter is the tail index. Fitting data to heavy tail distributions usually assumes independent observations. However, the most usual real market scenario describes clusters of extreme events rather than isolated records over some period of time. In that case, estimating tail probabilities includes estimating the extremal index. This chapter describes the usual extremal index estimators based in different approaches and illustrates their values for a real financial data set. Computations are provided by the use of suitable R packages.