Modeling tail risks and systemic risks using copulas

Abstract

Understanding the relationship between financial variables is an essential part of managing financial risk. Such relationships in the context of risk management are of sensation interest in the modern world in which modeling risk has become a popular idea. The 2007/08 financial meltdown has accentuated the importance of this because it showed that with a distant probability of an event happening, say 0.01%, it should not be overlooked. The existence of dependency between the two variables is underscored in their established joint distribution. Conventional financial models intensely depend on a relationship to elucidation the dependence that exists between tow variables. Nevertheless, as a means of measuring dependence, correlation entirely defines the dependence structure for normal distributions. This is more so in the case of elliptical distributions as opposed to other classes. Even within elliptical distributions, correlation remains delicate because it is easily distorted by outliers. One of the biggest shortfalls of current financial models is in their assumption and oversimplification that leads to false parameterization. Many financial models assume that asset returns and risk variables follow normal distribution and as such pay a_ention the judiciously possible (central moments), undermining the value of what is remotely probable (extreme events). Yet, the financial crisis showed that remote events are understated. Thus, this paper focuses on copula model- that characterized the dependence structure across the entire distribution. Also, copulas have the advantage of being able to portray more information concerning the dependence structures between the two variables because they are distributions themselves. From the viewpoint systemic and tail risk, the copula is motivating. In this regard, it enables us to disengage the dependence structure (linked with systemic risk) from the marginal distribution (linked with tail risk) and archetypal both distinctly with a bigger degree of precision. Fundamentally, copulas act as magnifying glasses that permit us to examine and model financial variables with greater precision- in this case the connections between systemic and tail risk