Modeling partial Greeks of variable annuities with dependence |
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Institution: | 1. Friedrich–Alexander University Erlangen-Nürnberg (FAU), Department of Insurance Economics and Risk Management, Lange Gasse 20, 90403 Nuremberg, Germany;2. Florida State University, Department of Risk Management/Insurance, Real Estate and Legal Studies, Tallahassee, FL, United States;1. Department of Mathematics, University of Illinois at Urbana–Champaign, United States;2. Faculty of Business and Economics, Katholieke Universiteit Leuven, Belgium;1. Department of Mathematics, University of Illinois at Urbana-Champaign, United States;2. Department of Risk Management & Insurance, Georgia State University, United States |
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Abstract: | Dynamic hedging used to mitigate the financial risks associated with large portfolios of variable annuities requires calculating partial dollar deltas on major market indices. Metamodeling approaches have been proposed in the past few years to address the computational issues related to the calculation of partial dollar deltas. In this paper, we investigate whether the additional complication of modeling the dependence between the partial dollar deltas improves the accuracy of the metamodeling approaches. We use several copulas to model the dependence structures of the partial dollar deltas and conduct numerical experiments to compare different metamodels. Despite the evidence of strong dependence in the estimated models, our numerical results show that modeling the dependence structures in the metamodels does not improve the accuracy of the estimations at the portfolio level. This is because the dependence between the partial dollar deltas is well captured by the covariates used in the marginal models. This finding suggests that we should focus more on marginal models than specifying the dependence structure explicitly. |
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Keywords: | Variable annuity Portfolio valuation Metamodeling Gamma distribution Copula |
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