Using Conditional Copula to Estimate Value Risk

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Review: Using Conditional Copula to Estimate Value at Risk
ActSc 991 Project
Changwu (Allen) Chen April 14, 2014
1 Introduction
Value at Risk (VaR) plays a central role in risk management. By definition, VaR is the maximum expected loss of a portfolio over a given time horizon with a certain confidence level. VaR can be seen as a quantile on the lower tail of the distribution of portfolio returns. Although VaR is a simple measure, it is not easily estimated.
There are several approaches for the estimation of VaR, such as historical simulations, the variance-covariance, and the Monte Carlo approaches. The first approach does not assume any underlying distribution, whereas the last two approaches demand the joint distribution to be known, which frequently assumed to be normal distribution. However, the deviation from normality could lead to an inadequate VaR estimate. In this case, the portfolio could be either riskier than desired or unnecessarily conservative.
The theory of copula is a powerful tool in modelling multivariate distributions be- cause it does not require the assumption of joint normality and it is a marginal free model. Copula have been broadly used in the statistical literature. And due to its simplicity and convenience, one may be interested in its application in the financial area.
In this paper I will first give a brief summary of the paper written by Helder Parra Palaro and Luiz Koodi Hotta [1]. Then I will discuss the key results presented in the paper

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