Financial Engineering: A New Longevity Bond to Manage Individual Longevity Risk

This paper proposes a new type of longevity bond as a post-retirement investment product for individuals to hedge their longevity risk which has the flexibility to meet both income and bequest needs. The payoffs of the bond are composed of flexible monthly coupon payments until death and a principal payment at the time of death. In order to price and hedge the bonds, we calibrate arbitrage-free Nelsen-Siegel (AFNS) interest rate and a multi-factor continuous time mortality model with Australian data. We show how to construct a hedging portfolio for a portfolio of these bonds issued to individuals with existing traded government and corporate bonds on the Australian market to minimize the interest rate risk. We also assess the capital requirements for the longevity risk and any remaining mismatching risk in the portfolio to quantify the capital cost to include in the individual bond price. The bond has the benefit of including a natural hedge through a principal payment on death and the flexibility to generate income with different patterns over older ages to meet increasing age care needs.