Market price of longevity risk for a multi-cohort mortality model with application to longevity bond

Speaker: Jonathan Ziveyi

The pricing of longevity-linked securities depends not only on stochastic processes followed by underlying factors, but also the attitude of investors towards the risk of those factors. In this research, we investigate how to derive the market risk premium of longevity risk using tradable retirement indexes. The multi-cohort mortality model is adopted where each factor is assigned a market price of mortality risk to compensate for liquidity constraints associated with mortality-linked instruments. To calibrate the market price of longevity risk, a common practice is to make use of some market prices, such as longevity-linked securities and longevity indices, since the market has been assuming an improvement in mortality. We use the BlackRock CoRI Retirement Indexes, which provides daily level of estimated cost of lifetime retirement income for 20 cohorts in U.S. For these 20 cohorts, risk premiums of the common factors are assumed to be the same across cohorts, but risk premium of the factor for specific cohort is allowed to take different values for different cohorts. Market price of longevity risk are then calibrated by matching the risk-neutral prices with index values. Simple closed-form expressions for European options on longevity zero-coupon bond are derived using the calibrated market price of longevity risk, which has important implication for hedging longevity risk with bond options.