Elliptical Distributions-based Estimation Of VaR And TCE

The large increase in the number of traded assets in the oortfolio of most financial institutions has made the measurement of market risk a primary concern for regulators and for intermal risk control. After being proposed in 1993, VaR approach has become the standerd for risk management industry. But VaR has various theoretical deficiencies as a measure of market risk. Conditional VaR(CVaR) and the subsequent TCE are alternative risk measure to the quantile which overcomes the theoretical deficiencies of VaR. In particular, this risk measure gives some information about the size of the size of the potential losses given that a loss bigger than VaR has occurred. This paper estimates and assesses tail-related risk using VaR, CVaR and TCE. Though VaR and CVaR has many compute methods, they have limitations. The characters of TCE under elliptical distribution are easily expressed though TCE has some limitations, too. We discuss the validity of VaR and give the most simple method of the test of the validity. According to the lemma of Neyman-Pearson, we give the statistical test of VaR. The paper introduces the theoretical basis and character of elliptical distribution. The corresponding expressions are gived according some known elliptical distribution(Normality, t-distribution , Logistic distribution and so on.). we have drawn some functional images , which describe the elliptical and its characters vividly. In particular, the Laplace and log-Laplace distributions are inducted. According their functions of density of probability, some researchs are spreaded. They enrich the scopes of TCE.