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ABSTRACT
Securitizing longevity/mortality risk can transfer Longevity /mortality risk to capital markets. Modeling and forecasting mortality rate is key to pricing mortality-linked securities. Catastrophic mortality and longevity jumps occur in historical data and have an important impact on security pricing. This article introduces a stochastic diffusion model with a double-exponential jump diffusion process that captures both asymmetric rate jumps up and down and also cohort effect in mortality trends. The model exhibits calibration advantages and mathematical tractability while better fitting the data. The model provides a closed-form pricing solution for J.P. Morgan's q-forward contract usable as a building block for hedging.
INTRODUCTION
The terms "longevity risk" and "mortality risk" have attracted the attention of insurance companies, annuity providers, pension funds, and investment banks. The definitions are as follows (Coughlan et al., 2007). Longevity risk describes the risk that an individual or group will live a longer life than expected (their mortality rate will be lower than expected), while mortality risk describes the risk that an individual or group will live a shorter life than expected their mortality rate will be higher than expected). Clearly, life insurers are interested in mortality risk while annuity providers, denned benefit plans and social insurance programs such as Social Security, are interested in longevity risk.
In the last several decades, life expectancy for populations in the developed world has, on average, been increasing by approximately 1.2 months every year. Globally, life expectancy at birth has increased by 4.5 months per year on average over the second half of the 20th century (Gutterman et al., 2002). Substantial improvements in longevity at older ages during the 20th century have challenged longevity risk management in pension funds that originally reserved using what would now be considered incorrectly diminished mortality rates. Further, documenting this issue, a 2006 study of the companies in the UK's FTSE100 index found that many companies had based their estimates of pension liabilities on mortality tables that underestimated expected lifetimes by not recognizing improving longevity, and that recognizing this underestimation of expected lifetimes would cause the aggregate deficit in pension reserves, to more than double from £46 billion to £100 billion (Tardine Lloyd Thompson, 2006). In 2010 alone, improved life expectancy added £5 billion to corporate pension obligations...