Cohort models of mortality and development of a tradable longevity market

摘要

Longevity-linked securities have received significant attention due to increasing demand for additional capacity and regulatory requirements. However, compared to the potential longevity risk exposure the size of present market remains small. In promoting the development of a liquid market for trading longevity risk, the primary focus of this thesis is to develop required methodologies and benchmarks for such a market. Specifically, this thesis consists of three parts.The first part proposes and calibrates a multi-cohort mortality model with a focus on financial applications. The proposed mortality model employs modelling techniques from interest rate theory, and can serve for the valuation of longevity-linked products. Furthermore, the model has many appealing features: i) it is a multi-cohort model that describes the whole mortality surface, ii) it captures cohort effects and allows for imperfect correlation between different cohorts, iii) it fits historical data at pension-related ages very well, and iv) it performs well in generating future survival curves.The second part develops value-based longevity indexes for multiple countries and assesses the basis risk of index-based longevity hedging implementation. A joint affine term structure mortality model is proposed for the construction of longevity indexes for different cohorts in domestic and foreign countries. Furthermore, we examine basis risk in index-based longevity hedges using a graphical risk metric which provides visual interpretations on the interplay between the portfolio to be hedged and the hedging instruments.Finally, with the mortality model proposed in the first part, the third part investigates how to calibrate the market price of longevity risk and its application to longevity bond option pricing. The model is extended to incorporate market prices of longevity risk corresponding to each model factors. We develop a new framework for the pricing and risk analysis of longevity-linked products allowing for stochastic longevity risk and interest rate factors. The proposed affine modelling framework can be used to price longevity-linked securities and derivatives, in particular, we derive prices for European options on longevity zero-coupon bonds.