%0 Journal Article
%T Modelling Annuity Portfolios and Longevity Risk with Extended CreditRisk$^+$
%A Jonas Hirz
%A Uwe Schmock
%A Pavel V. Shevchenko
%J Quantitative Finance
%D 2015
%I arXiv
%X Using an extended version of the credit risk model CreditRisk$^+$, we develop a flexible framework to estimate stochastic life tables and to model credit, life insurance and annuity portfolios, including actuarial reserves. Deaths are driven by common stochastic risk factors which may be interpreted as death causes like neoplasms, circulatory diseases or idiosyncratic components. Our approach provides an efficient, numerically stable algorithm for an exact calculation of the one-period loss distribution where various sources of risk are considered. As required by many regulators, we can then derive risk measures for the one-period loss distribution such as value at risk and expected shortfall. Using publicly available data, we provide estimation procedures for model parameters including classical approaches, as well as Markov chain Monte Carlo methods. We conclude with a real world example using Australian death data. In particular, our model allows stress testing and, therefore, offers insight into how certain health scenarios influence annuity payments of an insurer. Such scenarios may include outbreaks of epidemics, improvement in health treatment, or development of better medication. Further applications of our model include modelling of stochastic life tables with corresponding forecasts of death probabilities and demographic changes.
%U http://arxiv.org/abs/1505.04757v4