Measuring Economic Capital: Value-at-Risk, Expected Shortfall and Copula Approach

43 Pages Posted: 13 May 2011

See all articles by Jeungbo Shim

Jeungbo Shim

Illinois Wesleyan University

Seung-Hwan Lee

Illinois Wesleyan University

Richard D. MacMinn

National Chengchi University; The University of Texas

Date Written: May 12, 2011

Abstract

It is important to incorporate diverse heavy-tailed dependency between risks in estimating economic capital. Copulas can be a useful technique to capture dependence structure where extreme events occur simultaneously. Using the sample of U.S. property liability insurance industry, we examine the impact of different dependence structure between market risk and underwriting risk of insurance portfolio on the economic capital measured by Value-at-Risk (VaR) and Expected Shortfall (ES). We identify the type of copula that best fits the given application data and perform a goodness of fit test to assess the adequacy of the copula model selected. The results suggest that the grouped t copula is better performed than the standard t copula to describe the dependence structure in an insurance setting where different type of risk factors coexists. The result also shows the incremental diversification benefit in the joint modeling of underwriting risk and market risk compared to the modeling of market risk only considered, indicating that both risks diversify against one another to some degree.

Keywords: Economic Capital, Value-at-Risk, Grouped t Copula

JEL Classification: C00, C13

Suggested Citation

Shim, Jeungbo and Lee, Seung-Hwan and MacMinn, Richard D., Measuring Economic Capital: Value-at-Risk, Expected Shortfall and Copula Approach (May 12, 2011). Available at SSRN: https://ssrn.com/abstract=1840124 or http://dx.doi.org/10.2139/ssrn.1840124

Jeungbo Shim (Contact Author)

Illinois Wesleyan University ( email )

P.O. Box 2900
Bloomington, IL 61702-2900
United States

Seung-Hwan Lee

Illinois Wesleyan University ( email )

P.O. Box 2900
Bloomington, IL 61702-2900
United States

Richard D. MacMinn

National Chengchi University ( email )

Taipei
Taiwan

The University of Texas ( email )

2317 Speedway
Austin, TX 78712
United States

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