I have a doubt regarding tail dependence. Which Tail dependence ( upper or lower) will be more appropriate in measuring credit risk and why? Also, except to that to find the correlation between extreme events in the tail what are other importance of tail dependence? Thanks
You need to be clear about what is being measured before thinking about possible tail dependencies. Take default risk & consider corporate bonds as an example.... If we are looking at different tranches of debt issued by a single company and are modelling the time to default, then we might observe a high level of upper tail dependence because if one of the bonds defaults late in its term then the other is also likely to be defaulting late in its term. However, if we are looking at the returns on various corporate bonds issued by companies in different sectors it may be that there is a low level of upper tail dependence (high returns on one of the bonds is not necessarily associated with higher returns on the other, due to the diversification of credit risks in normal markets) but a high level of lower tail dependence (as in extreme markets all bonds may well suffer at the same time). So... it depends! Be careful... correlation (Pearson's) is not the same as dependence!!
Here is the question from a CERA past paper and I was too confused reading both the answer.! State whether lower or upper tail dependence is more relevant to credit default risk, and explain why. The asset return depends on sensitivity to one or more systematic (correlated) risks as well as one firm-specific (uncorrelated) risk. If a bad state of the world (increased systematic risk) leads to default for a particular asset, other assets are more likely to default as well, assuming they have a similar sensitivity to systematic risk. Therefore, credit default risk exhibits high lower tail dependence. In a good state of the world, systematic risk has little impact and the asset return is mostly affected by uncorrelated firm-specific risk. Independent or uncorrelated variables have no tail dependence. As such, credit default risk exhibits low upper tail dependence Can u please justify??? " http://www.soa.org/files/pdf/edu-2011-04-afe-sol.pdf "
