An empirical comparison of some experimental designs for the valuation of large variable annuity portfolios

Guojun Gan 1  and Emiliano A. Valdez 1
  • 1 Department of Mathematics, University of Connecticut


Variable annuities contain complex guarantees, whose fair market value cannot be calculated in closed form. To value the guarantees, insurance companies rely heavily on Monte Carlo simulation, which is extremely computationally demanding for large portfolios of variable annuity policies. Metamodeling approaches have been proposed to address these computational issues. An important step of metamodeling approaches is the experimental design that selects a small number of representative variable annuity policies for building metamodels. In this paper, we compare empirically several multivariate experimental design methods for the GB2 regression model, which has been recently discovered to be an attractive model to estimate the fair market value of variable annuity guarantees. Among the experimental design methods examined, we found that the data clustering method and the conditional Latin hypercube sampling method produce the most accurate results.

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  • [1] Barton, R. R. (2015). Tutorial: Simulation metamodeling. In Proceedings of the 2015 Winter Simulation Conference, pp. 1765–1779.

  • [2] Box, G. E. P. and N. R. Draper (2007). Response Surfaces, Mixtures, and Ridge Analyses. Second edition. Wiley, Hoboken NJ.

  • [3] Cathcart, M. J., H. Y. Lok, A. J. McNeil, and S. Morrison (2015). Calculating variable annuity liability “greeks” using Monte Carlo simulation. ASTIN Bull. 45(2), 239–266.

  • [4] Crombecq, K., E. Laermans, and T. Dhaene (2011). Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling. Eur. J. Oper. Res. 214(3), 683–696.

  • [5] Cummins, J., G. Dionne, J. B. McDonald, and B. Pritchett (1990). Applications of the GB2 family of distributions in modeling insurance loss processes. Insurance Math. Econ. 9(4), 257–272.

  • [6] de Jong, P. and G. Z. Heller (2008). Generalized Linear Models for Insurance Data. Cambridge University Press.

  • [7] Frees, E. W. (2009). Regression Modeling with Actuarial and Financial Applications. Cambridge University Press.

  • [8] Friedman, L. W. (1996). The Simulation Metamodel. Kluwer Academic Publishers, Norwell MA.

  • [9] Gan, G. (2011). Data Clustering in C++: an Object-Oriented Approach. Chapman & Hall/CRC, Boca Raton FL.

  • [10] Gan, G. (2013). Application of data clustering and machine learning in variable annuity valuation. Insurance Math. Econ. 53(3), 795–801.

  • [11] Gan, G. (2015a). Application of metamodeling to the valuation of large variable annuity portfolios. In Proceedings of the Winter Simulation Conference, pp. 1103–1114.

  • [12] Gan, G. (2015b). A multi-asset Monte Carlo simulation model for the valuation of variable annuities. In Proceedings of the Winter Simulation Conference, pp. 3162–3163.

  • [13] Gan, G., Q. Lan, and C. Ma (2016). Scalable clustering by truncated fuzzy c-means. BigDIA 1(2/3), 247–259.

  • [14] Gan, G. and X. S. Lin (2015). Valuation of large variable annuity portfolios under nested simulation: a functional data approach. Insurance Math. Econ. 62, 138–150.

  • [15] Gan, G. and X. S. Lin (2016). Efficient greek calculation of variable annuity portfolios for dynamic hedging: A two-level metamodeling approach. N. Am. Actuar. J., in press.

  • [16] Gan, G. and E. A. Valdez (2016, July). Regression modeling for the valuation of large variable annuity portfolios. Available at

  • [17] Hejazi, S. A. and K. R. Jackson (2016). A neural network approach to efficient valuation of large portfolios of variable annuities. Insurance Math. Econ. 70, 169–181.

  • [18] Khuri, A. I., B. Mukherjee, B. K. Sinha, and M. Ghosh (2006). Design issues for generalized linear models: a review. Stat. Sci. 21(3), 376–399.

  • [19] Kleiber, C. and S. Kotz (2003). Statistical Size Distributions in Economics and Actuarial Sciences. Wiley, Hoboken NJ.

  • [20] Kleijnen, J. P. C., S. M. Sanchez, T. W. Lucas, and T. M. Cioppa (2005). State-of-the-art review: a user’s guide to the brave new world of designing simulation experiments. INFORMS J. on Comp. 17(3), 263–289.

  • [21] Ledlie, M. C., D. P. Corry, G. S. Finkelstein, A. J. Ritchie, K. Su, and D. C. E. Wilson (2008). Variable annuities. Brit. Actuar. J. 14(2), 327–389.

  • [22] Loeppky, J. L., J. Sacks, and W. J. Welch (2009). Choosing the sample size of a computer experiment: A practical guide. Technometrics 51(4), 366–376.

  • [23] McCullagh, P. and J. A. Nelder (1989). Generalized Linear Models. Second edition. Chapman & Hall/CRC, Boca Raton FL.

  • [24] McKay, B. and I. Wanless (2008). A census of small latin hypercubes. SIAM J. Discrete Math. 22(2), 719–736.

  • [25] Minasny, B. and A. B. McBratney (2006). A conditioned latin hypercube method for sampling in the presence of ancillary information. Comp. & Geos. 32(9), 1378 – 1388.

  • [26] Myers, R. H. (1999, 01). Response surface methodology–current status and future directions. J. Qual. Tech. 31(1), 30–44.

  • [27] Myers, R. H., D. C. Montgomery, and C. M. Anderson-Cook (2009). Response Surface Methodology: Process and Product Optimization Using Designed Experiments. Third Edition. Wiley, Hoboken NJ.

  • [28] Olivieri, A. and E. Pitacco (2015). Introduction to InsuranceMathematics: Technical and Financial Features of Risk Transfers. Second Edition. Springer, New York.

  • [29] Phillips, P. (2012). Lessons learned about leveraging high performance computing for variable annuities. In Equity-Based Insurance Guarantees Conference, Chicago IL.

  • [30] Risk, J. and M. Ludkovski (2016). Statistical emulators for pricing and hedging longevity risk products. Insurance Math. Econ. 68, 45–60.

  • [31] Roudier, P. (2011). clhs: a R package for conditioned Latin hypercube sampling.

  • [32] Ryan, T. P. (2007). Modern Experimental Design. Wiley, Hoboken NJ.

  • [33] The Geneva Association Report (2013). Variable annuities - an analysis of financial stability. Available at https://www.

  • [34] Viana, F. (2013). Things youwanted to knowabout the Latin hypercube design and were afraid to ask. In 10thWorld Congress on Structural and Multidisciplinary Optimization, Orlando FL.


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