Valuation of large variable annuity portfolios: Monte Carlo simulation and synthetic datasets
Abstract
Metamodeling techniques have recently been proposed to address the computational issues related to the valuation of large portfolios of variable annuity contracts. However, it is extremely diffcult, if not impossible, for researchers to obtain real datasets frominsurance companies in order to test their metamodeling techniques on such real datasets and publish the results in academic journals. To facilitate the development and dissemination of research related to the effcient valuation of large variable annuity portfolios, this paper creates a large synthetic portfolio of variable annuity contracts based on the properties of real portfolios of variable annuities and implements a simple Monte Carlo simulation engine for valuing the synthetic portfolio. In addition, this paper presents fair market values and Greeks for the synthetic portfolio of variable annuity contracts that are important quantities for managing the financial risks associated with variable annuities. The resulting datasets can be used by researchers to test and compare the performance of various metamodeling techniques.
-
[1] Ahlgrim, K. C., S. P. D’Arcy, and R.W. Gorvett (2005). Modeling financial scenarios: A framework for the actuarial profession. Proceedings of the Casualty Actuarial Society 92(177), pp. 177-238.
-
[2] Ahlgrim, K. C., S. P. D’Arcy, and R. W. Gorvett (2008). A comparison of actuarial financial scenario generators. Variance 2(1), 111-134.
-
[3] Bacinello, A., P. Millossovich, A. Olivieri, and E. Pitacco (2011). Variable annuities: A unifying valuation approach. Insurance Math. Econom. 49(3), 285-297.
-
[4] Bacinello, A. R., P. Millossovich, and A. Montealegre (2016). The valuation of GMWB variable annuities under alternative fund distributions and policyholder behaviours. Scand. Actuar. J. 2016(5), 446-465.
-
[5] Bauer, D., A. Kling, and J. Russ (2008). A universal pricing framework for guaranteed minimum benefits in variable annuities. ASTIN Bull. 38(2), 621-651.
-
[6] Boyle, P. and M. Hardy (1997). Reserving formaturity guarantees: Two approaches. InsuranceMath. Econom. 21(2), 113-127.
-
[7] Brown, R. A., T. A. Campbell, and L. M. Gorski (2002). Valuation and capital requirements for guaranteed benefits in variable annuities. Record 28(3), Session 142OF.
-
[8] Carmona, R. and V. Durrelman (2006). Generalizing the Black-Scholes formula to multivariate contingent claims. J. Comput. Financ. 9(2), 43-67.
-
[9] 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.
-
[10] D’Arcy, S. P. and R. W. Gorvett (2000). Measuring the interest rate sensitivity of loss reserves. Proceedings of the Casualty Actuarial Society 87(167), pp. 365-400.
-
[11] Dardis, T. (2016). Model efficiency in the U.S. life insurance industry. The Modeling Platform 3, 9-16.
-
[12] Feng, R. and H. Huang (2016). Statutory financial reporting for variable annuity guaranteed death benefits:Market practice, mathematical modeling and computation. Insurance Math. Econom. 67, 54-64.
-
[13] Feng, R. and Y. Shimizu (2016). Applications of central limit theorems for equity-linked insurance. Insurance Math. Econom. 69, 138-148.
-
[14] Feng, R. and H. Volkmer (2012). Analytical calculation of risk measures for variable annuity guaranteed benefits. Insurance Math. Econom. 51(3), 636-648.
-
[15] Gan, G. (2013). Application of data clustering and machine learning in variable annuity valuation. Insurance Math. Econom. 53(3), 795-801.
-
[16] Gan, G. (2015a). Application of metamodeling to the valuation of large variable annuity portfolios. Proceedings of the Winter Simulation Conference, pp. 1103-1114.
-
[17] Gan, G. (2015b). A multi-asset Monte Carlo simulation model for the valuation of variable annuities. Proceedings of the 2015 Winter Simulation Conference, pp. 3162-3163.
-
[18] Gan, G. (2017). An Introduction to Excel VBA Programming: With Application in Finance and Insurance. CRC Press, Boca Raton FL.
-
[19] Gan, G. and J. Huang (2017). A data mining framework for valuing large portfolios of variable annuities. Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1467-1475.
-
[20] Gan, G. and X. S. Lin (2015). Valuation of large variable annuity portfolios under nested simulation: A functional data approach. Insurance Math. Econom. 62, 138-150.
-
[21] 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. 21(2), 161-177.
-
[22] Gan, G. and E. A. Valdez (2016). An empirical comparison of some experimental designs for the valuation of large variable annuity portfolios. Depend. Model. 4(1), 382-400.
-
[23] Gan, G. and E. A. Valdez (2017). Regression modeling for the valuation of large variable annuity portfolios. N. Am. Actuar. J. In press.
-
[24] Gerber, H. and E. Shiu (2003). Pricing lookback options and dynamic guarantees. N. Am. Actuar. J. 7(1), 48-66.
-
[25] Hagan, P. S. and G. West (2006). Interpolation methods for curve construction. Appl. Math. Finan. 13(2), 89-129.
-
[26] Hardy, M. (2003). Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance. John Wiley & Sons, Hoboken NJ.
-
[27] Hejazi, S. A. and K. R. Jackson (2016). A neural network approach to efficient valuation of large portfolios of variable annuities. Insurance Math. Econom. 70, 169-181.
-
[28] Hejazi, S. A., K. R. Jackson, and G. Gan (2017). A spatial interpolation framework for efficient valuation of large portfolios of variable annuities. Quant. Financ. Econ. 1(2), 125-144.
-
[29] 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.
-
[30] Marshall, C., M. Hardy, and D. Saunders (2010). Valuation of a guaranteed minimum income benefit. N. Am. Actuar. J. 14(1), 38-58.
-
[31] Shevchenko, P. V. and X. Luo (2016). A unified pricing of variable annuity guarantees under the optimal stochastic control framework. Risks 4(3), 22.
-
[32] The Geneva Association (2013). Variable Annuities - An Analysis of Financial Stability. The Geneva Association.
-
[33] Varnell, E. M. (2011). Economic scenario generators and solvency II. Brit. Actuar. J. 16(1), 121-159.
