Article2013

Annuity Uncertainty with Stochastic Mortality and Interest Rates

10 citations0/0 files storedNorth American Actuarial Journal

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Insurance, Mortality, Demography, Risk Management Stochastic processes and financial applications Probability and Risk Models

Abstract

Risk analysis in actuarial science has shifted its focus from diversifiable risk to systematic risk in the last 20 years or so. This article contributes further in this direction by proposing the concept of annuity rate to take account of systematic risk inherent in annuity products. The annuity rate is the conditional expectation of the annuity’s future payments, given the future paths of mortality and interest rates. We provide an empirical study to investigate the impact of the two systematic risk factors on the distribution of the annuity rate. In particular, we adopt the Lee-Carter and the Cairns-Blake-Dowd models for mortality risk, and the one-factor and two-factor CIR models for interest risk. Monte Carlo simulation is used to provide numerical illustrations of sensitivity analysis of the annuity rate and of risk assessment of a guaranteed annuity option.

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References

1993Dynamic Asset Pricing Theory.1992Modeling and Forecasting U. S. Mortality 1992An Empirical Comparison of Alternative Models of the Short-Term Interest Rate 2006A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration 2002A Poisson log-bilinear regression approach to the construction of projected lifetables 2009A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States 2000A universal pattern of mortality decline in the G7 countries 2001Evaluating the Performance of the Lee-Carter Method for Forecasting Mortality

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