Journal of Risk Model Validation

Model risk in mortality-linked contingent claims pricing

Gareth W Peters, Hongxuan Yan and Jennifer Chan

  • The authors demonstrate for the U.K., U.S.A. and Australia that we are able to reduce the model risk and associated forecast errors of classical Lee-Carter models in constructing forecasts for mortality and subsequent life expectancy by age and gender. This is achieved by developing new classes of multivariate long-memory models for mortality which we compare to extensions of classical Lee-Carter models.
  • A classical and standard short rate one factor model for interest rates is used, and we add the novel component of incorporating dependence links with our stochastic mortality models. A Bayesian calibration and forecasting framework which is estimated with a Hamiltonian Markov Chain Monte Carlo sampling procedure is developed.
  • These frameworks are used to study the influence of model risk for life products including annuity portfolios and the valuation of a guaranteed annuity option (GAO). It is demonstrated that classical Lee-Carter type models can produce less accurate model forecasts than the proposed models and the mispricing cost of this model risk is quantified.

Pricing mortality-linked contingent claims depends critically on the ability to accurately model three core stochastic components: expected mortality rates and life expectancy by age group, for a given population; interest rate dynamics over various time horizons; and the causal relationship between mortality events and interest rate fluctuations. In each of these components, there is potential for model misspecification that manifests as model risk and may result in mispricing. We study the influence of model risk on pricing life products, including annuity portfolios and guaranteed annuity options. We demonstrate that classical Lee–Carter-type models can produce less accurate model forecasts than our proposed multivariate long-memory models and we quantify the mispricing cost of this model risk.

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