Affine Stochastic Mortality

Abstract

We propose a new model for stochastic mortality. The model is based on the literature on a¢ ne term structure models. It satis…es three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with …nancial option pricing models. We test the model …t using data on Dutch mortality rates. Furthermore, we discuss the speci…cation of a market price of mortality risk and apply the model to the pricing of a Guaranteed Annuity Option and the calculation of required Economic Capital for mortality risk.

A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration

“…Models following the approach of Lee and Carter typically adapt discrete‐time time series models to capture the random element in the stochastic development of mortality rates. Other authors have developed models in a continuous‐time framework (see, for example, Milevsky and Promislow, 2001; Dahl, 2004; Dahl and Møller, 2005; Miltersen and Persson, 2005; Biffis, 2005; Schrager, 2006). For further discussion and a review of previous work, the reader is referred to Cairns, Blake, and Dowd (2006).…”

Pricing Mortality Securities With Correlated Mortality Indexes

“…Moreover, the existing mortality literature has demonstrated the significance of catastrophic death events in the pricing and tranche structure for a mortality risk bond (Cox, Lin, and Wang, ; Bauer and Kramer, ; Chen and Cox, ). While longevity risk modeling usually simplifies the analysis by ignoring dramatic mortality changes (Cairns, Blake, and Dowd, ; Schrager, ; Kogure and Kurachi, ; Wills and Sherris, ; Yang, Yue, and Huang, ; Cox et al, ), mortality jumps must be considered in order to successfully structure and price mortality‐linked securities. Thus, in this article, as the first objective, we develop a tractable mortality model, which captures the mortality correlations among countries and incorporates mortality jumps.…”

Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio

“…Olivieri (2001) examines the implications of this uncertainty for the required reserves for insurance and annuity polices. In related work, Milevsky and Promislow (2001), Dahl (2004), Schrager (2006), Ballota and Haberman (2003) as well as Biffis and Millossovich (2004) use continuous‐time modeling for the hazard rate to develop pricing formulae for options that are embedded within various insurance and annuity policies. Likewise, Denuit and Dhaene (2006) use comonotonicity methods to compute probabilities, conditional tail expectations and values‐at‐risk for portfolios of dependent insurance policies.…”