A Multifactor Generalisation of the Olivier-Smith Model for Stochastic Mortality

Recent years have seen the development of a number of models for the future development of aggregate mortality rates. Amongst these the Olivier and Smith model (Olivier and Jeffery, 2004, and Smith, 2005) was developed within the forward-rate framework discussed by Cairns et al. (2006) and Miltersen and Persson (2005). This model has a numbe of useful properties that make it a very good model for use in the valuation of life insurance contracts that incorporate embedded options. We discuss here a generalisation of the Olivier and Smith model. Dynamics of the model in its published form are driven by a sequence of univariate gamma random variables. We demonstrate that the model in this form does not adequately match historical data. We discuss a generalisation of the model that uses multivariate Gamma random variables as drivers. This approach potentially gives us much greater control over the term structure of volatility of spot survival probabilities and over the correlation term structure. We introduce a possible approach for simulation of multivariate gamma random variables that facilitates A Generalisation of the Olivier-Smith Model 2