The effect of secondary markets on equity-linked life insurance with surrender guarantees

We study the effect of secondary markets on equity-linked life insurance contracts with surrender guarantees. The policyholders are assumed to be boundedly rational in giving up their contracts, and a proportion of policyholders will access the secondary markets instead of surrendering the contracts to the insurance company. We formulate the valuation problems from both the insurance company's and the policyholders' perspectives and characterize the contract values by deriving the respective pricing PDEs. Comparative statics are derived indicating the effect of the level of the policyholder's rationality and secondary market characteristics such as accessibility and competition on the contract values. The pricing PDEs are solved numerically via the Crank-Nicolson scheme to study the implication of the inclusion of a secondary market. We show that a secondary market generally increases the risk borne by the insurance company and the policyholders profit from the secondary market only when the secondary market is sufficiently competitive. Furthermore, we derive the necessary condition for the existence of a fair contract in this context and study the effect of the secondary market on fair contract design.