The Estimates Of Lower And Upper Bounds Of The Value-at-Risk For Functions Of Dependent Risks

In the field of finance, investors prefer the portfolios comprised of several kindsof financial products to a single one, in order to reduce the risk or averse the riskbecause of the dependence between the different risks. Among risk management, riskmeasuring is the most important one. Due to its simplicity and understood easily, butalso because of regulatory reasons, Value-at-Risk (VaR) remains one of the mostpopular risk measures. In the past years, the theory of copula, which has been appliedto many areas including financial field, is known to provide a useful tool for riskanalysis. Its character of dividing the joint distribution into two parts, marginaldistribution and dependence structure, will make it develop and applied widely andquickly.Taking Value-at-Risk as a risk measure, this article, based on theory of copula,show the best-possible bounds of VaR at certain level for functions of dependent risksof UK Sterling/US Dollar and UK Sterling/Canadian Dollar. The rank coefficientKendall Ï„ is criterion of comparing the dependence of different kinds of copula. Themethod used in this paper can easily be adapted for risk measures different from VaRand portfolios consisting of more financial products.