Using Conditional Copula to Estimate Value at Risk

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.

Portfolio value‐at‐risk estimation for spot chartering decisions under changing trade patterns: A copula approach

“…When calculating VaR using parametric methods, the assumption of a joint multivariate distribution is crucial. The traditional portfolio VaR model often assumes a normal joint distribution, which in reality is rarely the case, as financial asset returns often exhibit skewness and fat tail behaviors (Palaro & Hotta, 2006). As a result, assuming a multivariate normal distribution often leads decisionmakers to underestimate VaR.…”

Analisis Value at Risk (VaR) pada Investasi Saham Blue Chips dengan Pendekatan Copula

“…Copula adalah suatu fungsi yang menghubungkan fungsi distribusi multivariat dengan distribusi marginalnya [10]. Teori copula sendiri merupakan alat yang dapat memodelkan distribusi bersama karena tidak memerlukan asumsi normalitas bersama dan memungkinkan bila pemecahan setiap distribusi bersama n-dimensi kedalam distribusi marginal n dan sebuah fungsi copula [11].…”

Correlation analysis of financial assets based on asymmetric copula

“…In addition, Patton [4] proposed the definition of conditional copula and used it to characterize the asymmetric dependence structure between exchange rates. Palaro and Hotta [5] used the conditional copula to dynamically analyze the dependence relationship among financial assets. Nikolai et al [6] summarized in detail the development and application of copula function in recent years and made a reasonable prospect for its future development.…”