Modeling longevity risk transfers as Nash bargaining problems: Methodology and insights

Abstract

The problem of longevity risk has recently received considerable attention. In this paper, we apply economic modeling methods to longevity risk securitization, which is now regarded by pension and insurance industries as a solution to the problem. Specifically, we model the trade of a longevity security as a two-player bargaining game, and use Nash's bargaining solution to determine the outcome of it. Our work not only offers an alternative method for pricing longevity securities, but also reveals several properties about the market for longevity securities. First, a trade would occur if the longevity security is an effective hedging instrument, and the trade would benefit all agents involved. Second, a trade of longevity risk can reduce pension plans' bankruptcy risk, safeguarding the financial security of pension plan members. Finally, compared to the competitive equilibrium, Nash's bargaining solution yields higher trading prices. Therefore, as the market becomes more competitive, pension plans may hedge longevity risk at a lower cost.