A variable annuity is a popular life insurance product that comes with financial guarantees. Using Monte Carlo simulation to value a large variable annuity portfolio is extremely time-consuming. Metamodeling approaches have been proposed in the literature to speed up the valuation process. In metamodeling, a metamodel is first fitted to a small number of variable annuity contracts and then used to predict the values of all other contracts. However, metamodels that have been investigated in the literature are sophisticated predictive models. In this paper, we investigate the use of linear regression models with interaction effects for the valuation of large variable annuity portfolios. Our numerical results show that linear regression models with interactions are able to produce accurate predictions and can be useful additions to the toolbox of metamodels that insurance companies can use to speed up the valuation of large VA portfolios.

Dynamic hedging has been adopted by many insurance companies to mitigate the financial risks associated with variable annuity guarantees. In order to simulate the performance of dynamic hedging for variable annuity products, insurance companies rely on nested stochastic projections, which is highly computationally intensive and often prohibitive for large variable annuity portfolios. Metamodeling techniques have recently been proposed to address the computational issues. However, it is difficult for researchers to obtain real datasets from insurance companies to test metamodeling techniques and publish the results in academic journals. In this paper, we create synthetic datasets that can be used for the purpose of addressing the computational issues associated with the nested stochastic valuation of large variable annuity portfolios. The runtime used to create these synthetic datasets would be about 3 years if a single CPU were used. These datasets are readily available to researchers and practitioners so that they can focus on testing metamodeling techniques.

For automobile insurance, it has long been implied that when a policyholder made at least one claim in the prior year, the subsequent premium is likely to increase. When this happens, the policyholder may seek to switch to another insurance company to possibly avoid paying for a higher premium. In such situations, insurers may be faced with the challenges of policyholder retention by keeping premiums low in the face of competition. In this paper, we seek to find empirical evidence of possible association between policyholder switching after a claim and the associated change in premium. In accomplishing this goal, we employ the method of association rule learning, a data mining technique that has its origins in marketing for analyzing and understanding consumer purchase behavior. We apply this unique technique in two stages. In the first stage, we identify policyholder and vehicle characteristics that affect the size of the claim and resulting change in premium regardless of policy switch. In the second stage, together with policyholder and vehicle characteristics, we identify the association among the size of the claim, the level of premium increase and policy switch. This empirical process is often challenging to insurers because they are unable to observe the new premium for those policyholders who switched. However, we used a 9-year claims data for the entire Singapore automobile insurance market that allowed us to track information before and after the switch. Our results provide evidence of a strong association among the size of the claim, the level of premium increase and policy switch. We attribute this to the possible inefficiency of the insurance market because of the lack of sharing and exchange of claims history among the companies.