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Using Conditional Copula to Estimate Value at Risk

Journal of Data Science 4(2006), 93-115

23 Pages Posted: 13 Oct 2005 Last revised: 19 Oct 2013

Helder P. Palaro

Independent

Luiz Koodi Hotta

University of Campinas (UNICAMP) - Department of Statistics

Date Written: November 21, 2004

Abstract

Value at Risk (VaR) plays a central role in risk management. There are several approaches for the estimation of VaR, such as historical simulation, the variance-covariance (also known as analytical), and the Monte Carlo approaches. Whereas the first approach does not assume any distribution, the last two approaches demand the joint distribution to be known, which in the analytical approach is frequently the normal distribution. The copula theory is a fundamental tool in modeling multivariate distributions. It allows the definition of the joint distribution through the marginal distributions and the dependence between the variables. Recently the copula theory has been extended to the conditional case, allowing the use of copulae to model dynamical structures. Time variation in the first and second conditional moments is widely discussed in the literature, so allowing the time variation in the conditional dependence seems to be natural. This work presents some concepts and properties of copula functions and an application of the copula theory in the estimation of VaR of a portfolio composed by Nasdaq and S&P500 stock indices.

Keywords: Copula, multivariate distribution function, value-at-risk

JEL Classification: C15, D81, G10

Suggested Citation

Palaro, Helder P. and Hotta, Luiz Koodi, Using Conditional Copula to Estimate Value at Risk (November 21, 2004). Journal of Data Science 4(2006), 93-115. Available at SSRN: https://ssrn.com/abstract=818884 or http://dx.doi.org/10.2139/ssrn.818884

Helder Palaro (Contact Author)

Independent ( email )

Monaco

Luiz Hotta

University of Campinas (UNICAMP) - Department of Statistics ( email )

Campinas, São Paulo 13083-859
Brazil

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