Tail dependence measure for examining financial extreme co-movements

Alexandru V Asimit,Russell Gerrard,Yanxi Hou,Liang Peng

doi:10.1016/j.jeconom.2016.05.011

Abstract

Modeling and forecasting extreme co-movements in financial market is important for conducting stress test in risk management. Asymptotic independence and asymptotic dependence behave drastically different in modeling such co-movements. For example, the impact of extreme events is usually overestimated whenever asymptotic dependence is wrongly assumed. On the other hand, the impact is seriously underestimated whenever the data is misspecified as asymptotic independent. Therefore, distinguishing between asymptotic independence/dependence scenarios is very informative for any decision-making and especially in risk management. We investigate the properties of the limiting conditional Kendall’s tau which can be used to detect the presence of asymptotic independence/dependence. We also propose nonparametric estimation for this new measure and derive its asymptotic limit. A simulation study shows good performances of the new measure and its combination with the coefficient of tail dependence proposed by Ledford and Tawn (1996, 1997). Finally, applications to financial and insurance data are provided.

Highlights

An important task in risk management is to understand the reliability of the proposed model in the presence of adverse scenarios, known as stress testing
Our proposal appeals to a robust measure of association that is appealing to a wide audience, and we find that most of the extreme scenarios are characterized by our method in order to elaborate an alternative way to characterize the asymptotic independence and asymptotic dependence
We investigate the relationship between tail dependence and the conditional version of a classical measure of association, namely Kendall’s tau

Summary

Introduction

An important task in risk management is to understand the reliability of the proposed model in the presence of adverse scenarios, known as stress testing. Which makes extrapolation, i.e. statistical inference, impossible for concomitant extreme sets In this case, F is said to have the asymptotic independence property, and a different convergence rate condition in (1.3) is needed for predicting joint extreme events. It is known that testing asymptotic dependence is extremely challenging due to limited observations in the tail region, and so it is always desirable to have some alternative measures and competitive statistical methods. Study of conditional Kendall’s tau for a fixed level u is relatively known in the literature (see Venter, 2001 and Gijbels et al, 2011) It remains unknown whether there exists some relationship between the limit of this conditional measure and asymptotic dependence, and how to estimate the limit.

Main Results

Examples

Simulation study

Real data analysis

Proofs