Longevity/mortality Risk Modeling and Securities Pricing

Article excerpt

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, defined 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 [pounds sterling] to 100 billion [pounds sterling] (Jardine Lloyd Thompson, 2006). In 2010 alone, improved life expectancy added 5 billion [pounds sterling] to corporate pension obligations in the United Kingdom (Reuters News Service, 2010). In the United States, according to Watson Wyatt, the implementation of the recently established Internal Revenue Service's (IRS) mortality assumptions for the level of pension contributions needed for adequate reserving will increase pension liabilities by 5-10 percent (Halonen, 2007). Similarly, Mercer Human Resource Consulting has calculated that the use of up-to-date mortality tables would increase the cost of providing a pension to a male born in 1950 by 8 percent (Smithson, 2006).

On the other side of the mortality/longevity risk problem, many life insurers globally have become concerned about their potential exposure to catastrophic mortality risks, such as flu. During the 1918 flu, more than 675,000 excess deaths from the flu occurred between September 1918 and April 1919 in the United States alone, causing a huge jump in the mortality rate time series. More recently, H5N1 avian influenza occurred in Hong Kong in 1997, and HIN1 occurred globally in 2009. According to the American Council of Life Insurers (ACLI), in 2009, the reserves for U.S. life insurance policies were around $3.8 trillion (ACLI, 2010); however, there is a possibility that a major pandemic event could trigger insolvency in the life insurance industry, and this situation worsens if catastrophic mortality events coincide with financial downturns (Toole, 2007)

The interaction of the insurance industry and the capital markets (Cummins, 2005) has provided a vehicle for mitigating the above mentioned mortality/longevity risk, namely, through the financial securitization (cf. …