Application of metamodeling to the valuation of large variable annuity portfolios

Abstract

Variable annuities are long-term investment vehicles that have grown rapidly in popularity recently. One major feature of variable annuities is that they contain guarantees. The guarantees embedded in variable annuities are complex and the values of the guarantees cannot be obtained from closed-form formulas. Insurance companies rely heavily on Monte Carlo simulation to calculate the fair market values of the guarantees. Valuation and risk management of a large portfolio of variable annuities are a big challenge to insurance companies because the Monte Carlo simulation model is very time consuming. In this paper, we propose to use a metamodeling approach to speed up the valuation of large portfolios of variable annuities. Our numerical results show that the metamodeling approach can reduce the runtime significantly and produce accurate approximations.

Valuation of Large Variable Annuity Portfolios Using Linear Models with Interactions

“…Gan (2013) Clustering Kriging Gan and Lin (2015) Clustering Kriging Gan (2015) LHS Kriging Hejazi and Jackson (2016) Uniform sampling Neural network Gan and Valdez (2016) Clustering, LHS GB2 regression Gan and Valdez (2017a) Clustering Gamma regression Gan and Lin (2017) LHS, conditional LHS Kriging Hejazi et al (2017) Uniform sampling Kriging, IDW, RBF Gan and Huang (2017) Clustering Kriging Xu et al (2018) Random sampling Neural network, regression trees Gan and Valdez (2018) Clustering GB2 regression…”

“…Since the k-prototype algorithm is not efficient for selecting a moderate number (e.g., 200) of representative VA contracts, Gan (2015) studied the use of Latin hypercube sampling (LHS) for selecting representative contracts. Gan and Huang (2017) used the truncated fuzzy c-means (TFMC) algorithm, which is a scalable clustering algorithm developed by , to select representative contracts.…”

“…See, for example, Gan (2013); Gan and Lin (2015); Gan (2015); Hejazi and Jackson (2016); Gan and Valdez (2016); Gan and Valdez (2017a); Gan and Lin (2017); Hejazi et al (2017); Gan and Huang (2017); Xu et al (2018);and Gan and Valdez (2018). In metamodeling, a metamodel, which is a model of the Monte Carlo simulation model, is built to replace the Monte Carlo simulation model to value the VA contracts in a large portfolio.…”

A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities

“…The proposed methods in (Gan and Lin, 2015;Gan, 2013Gan, , 2015 can be categorized under the general framework of spatial interpolation. Spatial interpolation is the procedure of estimating the value of data at unknown locations in space given the observations at sampled locations (Burrough et al, 1998).…”

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

“…In these metamodeling methods, a clustering method was used to select representative VA policies. In [11], a Latin hypercube sampling method was used to select representative VA policies. In [15], a two-level metamodeling method was proposed to estimate the dollar deltas e ciently for dynamic hedging purpose.…”