Assessing Lapse Risk and Fair Market Value of Life Insurance Contracts with Surrender Guarantees
Final Report Abstract
The financial crisis beginning in 2008 put the spotlight on insurance companies as well as banks. Regulators of the financial service industry enforced stricter control by demanding more detailed risk reports and increasing capital requirements. In addition, consumers reassessed their investment preferences and withdrew wealth from financial contracts, such as savings schemes and pension plans. In this context, the project addressed the premature ending of life insurance contracts with surrender guarantees, also known as surrender or lapsing. Lapse risk was and still is a major risk factor according to the relevant regulation Solvency II, as of 2019. This project emphasizes the understanding of policyholders’ lapse behaviour. In contrast to past approaches, where lapse occurs in a statistical fashion, or, in an optimal way, that is, the policyholder exercises the option to lapse optimally, this project characterizes policyholders as inattentive, thinking about exercising the lapse option only sporadically, at random intervention times. The motivation for this specification is that policyholders are in general no finance experts and have only partial access to relevant information, summarized under inattention. The key contribution of this project is the provision of a general Markovian model to value American-style contracts under inattention. Exercise decisions maximizing the contract’s payoff are not admissible continuously but at random intervention times arriving with possibly state and time dependent intensities. We provide useful characterizations of the policyholder’s surrender strategy as well as various numerical approaches. In particular, our suitably adapted least square Monte Carlo (LSM) method is applicable to complex and possibly high-dimensional settings, necessary for practically relevant application. Further, we extend the latter results by allowing the policyholder to allocate attention optimally. We can summarize this under the term rational inattention. The derived results are especially relevant to lapse risk modelling, but are also applicable to decision-making in general. Finally, we contribute to the understanding of the surrender behavior in life insurance contracts by incorporating contagious surrender behavior into the pricing and regulation of participating life insurance contracts. Here, we focus on a financially sophisticated professional policyholder and several retail policyholders, such that the respective surrender behavior depend on each other. While the professional’s strategy exploits retail policyholders, the latter benefit from a regulatory intervention. Our results provide guidance for regulators on how to protect retail investors in this specific situation. Furthermore, the project contributes to the related field of dependence modelling in insurance as well as finance, which is particularly important in risk measurement and risk management. We provide a framework for sophisticated dependence modelling in continuous time. In particular, we use information flow as a latent factor affecting the directing process, that is, the change in risk factors conditional on the information flow. In an empirical strand of the project, we also show how to measure extremal dependence, as a specific example in the shipping market, for a better understanding of the occurrence of crises.
Publications
- „Marginal Consistent Dependence Modelling Using Weak Subordination for Brownian Motions“, Quantitative Finance 18(11), S. 1909–1925, 2018
M. Michaelsen und A. Szimayer
(See online at https://doi.org/10.1080/14697688.2018.1439182) - „Measuring Crisis Risk Using Conditional Copulas: An Empirical Analysis of the 2008 Shipping Crisis”, Journal of Applied Econometrics 33(2), S. 271–289, 2018
S. Opitz, H. Seidel und A. Szimayer
(See online at https://doi.org/10.1002/jae.2609)
