Tail dependence measure for examining financial extreme co-movements

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.

Telling tales from the tails: High‐dimensional tail interdependence

“…The equivalence of the CTI and the tail dependence coefficient in the limit is an important finding that connects our framework to the literature on the multivariate extreme value theory (e.g., Asimit et al, 2016;Bücher et al, 2015). We will pursue this avenue in future research.…”

“…The most widely applied dependence measure, Pearson's correlation coefficient, is an inadequate measure in many situations as it captures only the linear dependence between pairs of random variables (e.g., Longin & Solnik, 2001). Extreme dependence has been captured by copulas (e.g., Nelsen, 2007;Opitz, Seidel, & Szimayer, 2017;Patton, 2006), multivariate quantile regressions (e.g., White, Kim, & Manganelli, 2015), and multivariate extreme-value theory (e.g., Asimit, Gerrard, Hou, & Peng, 2016;Bücher, Jäschke, & Wied, 2015;Jansen & de Vries, 1991). However, these measures of dependence are generally feasible only in low dimensions.…”

Tail dependence of the Gaussian copula revisited

“…We conclude this section by noting that other scholars have also considered other than the diagonal paths when measuring tail dependence. For example, Asimit et al (2016) use the conditional Kendall's tau to measure tail dependence. Joe et al (2010) introduce the tail dependence function b(w 1 , w 2 ; C) = lim u↓0 C(uw 1 , uw 2 )/u for w 1 , w 2 > 0 to measure tail dependence via different directions.…”

On kernel-based estimation of conditional Kendall’s tau: finite-distance bounds and asymptotic behavior

“…Nonetheless, such pointwise events can be found in the literature, but in some parametric or semi-parametric particular frameworks, as for the identifiability of frailty distributions in bivariate proportional models ( [18], [19]). Other related papers are [20] or [21], that are dealing with extreme co-movements (bivariate extreme-value theory). There, the tail conditioning events of Kendall's tau have probabilities that go to zero with the sample size.…”