Yajing Xu, Michael Sherris and Jonathan Ziveyi
The pricing of longevity-linked securities depends not only on the stochastic uncertainty of the underlying risk factors, but also the attitude of investors towards those factors. In this research, we investigate how to estimate the market risk premium of longevity risk using investable retirement indexes, incorporating uncertain real interest rates using an affine dynamic Nelson-Siegel model. A multi-cohort aggregate, or systematic, continuous time affine mortality model is used where each risk factor is assigned a market price of mortality risk. To calibrate the market price of longevity risk, a common practice is to make use of market prices, such as longevity-linked securities and longevity indices. We use the BlackRock CoRI Retirement Indexes, which provides a daily level of estimated cost of lifetime retirement income for 20 cohorts in the U.S. Although investment in the index directly is not possible, individuals can invest in funds that track the index. For these 20 cohorts, we assume risk premiums for the common factors are the same across cohorts, but the risk premium of the factors for a specific cohort is allowed to take different values for different cohorts. The market prices of longevity risk are then calibrated by matching the risk-neutral model prices with BlackRock CoRI index values. Closed-form expressions and prices for European options on longevity zero-coupon bonds are derived using the model and compared to prices for standard options on zero coupon bonds. The impact of uncertain mortality on long term option prices is quantified and discussed.
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