Multiple Change-Points Test For The Dependence Structures Of Portfolio

In the field of finance, a large number of financial instruments hold the un-certain profits, i.e. the risks. Dependence plays an important role in risk man-agement. In the past, people only used linear correlation to measure dependence.However, with the risk management getting more and more complicated, the studyof dependence with linear correlation alone is far away from the modern risk super-intendent's satisfaction. They must go deep into understanding other dependenceconcepts, such as rank correlation.In order to model more general dependence concepts, Sklar provide Copula todescribe the dependence better than the correlation. Copula gradually becomesa useful tool for risk analysis because of its special character that it divides thejoint distribution into marginal distribution and dependence structure.In financial markets, the price movements of di?erent assets are often related.Financial crises, market deregulations, policy shifts may cause changes in the wayfinancial asset prices relate with each other. There is considerable interest in thedynamic behavior of correlation between di?erent risks as a function of time.In this paper we use the Mixed Gumble Copula to create an appropriatemodel to describe the dependence of the exchange rates of the English Poundand Eurodollar. Then we will discuss the changes in dependence structure whichwe model by using change-point techniques. This methodology applies in manyfinancial fields such as capital pricing and risk management.