Dependency between Risks and the Insurer’s Economic Capital: A Copula-based GARCH Model

Shim Jeungbo () and Lee Seung-Hwan ()
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Shim Jeungbo: Business School, University of Colorado-Denver, 1475 Lawrence Street, Denver, CO 80202, USA
Lee Seung-Hwan: Department of Mathematics, Illinois Wesleyan University, Bloomington, IL, USA

Asia-Pacific Journal of Risk and Insurance, 2017, vol. 11, issue 1, 29

Abstract: Copulas can be a useful tool to capture heavy-tailed dependence between risks in estimating economic capital. This paper provides a procedure of combining copula with GARCH model to construct a multivariate distribution. The copula-based GARCH model using a skewed student’s t-distribution controls for the issues of skewness, heavy tails, volatility clustering and conditional dependencies contained in the financial time series data. Using the sample of U.S. property liability insurance industry, we perform Monte Carlo simulation to estimate the insurer’s economic capital measured by Value-at-Risk (VaR) and Expected Shortfall (ES). The result indicates that the choice of dependence structure and business mix between asset classes and liability lines has a significant impact on the resulting capital requirements and diversification benefits. We find the incremental diversification benefit in terms of a reduction in the total capital requirement from the joint modeling of underwriting risk and market risk compared to the modeling of market risk only.

Keywords: economic capital; Value-at-Risk; copula; GARCH model; diversification (search for similar items in EconPapers)
JEL-codes: C00 C13 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1515/apjri-2016-0021

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