Pricing Mortality Securities With Correlated Mortality Indexes

Abstract

This article proposes a stochastic model, which captures mortality correlations across countries and common mortality shocks, for analyzing catastrophe mortality contingent claims. To estimate our model, we apply particle filtering, a general technique that has wide applications in non-Gaussian and multivariate jump-diffusion models and models with nonanalytic observation equations. In addition, we illustrate how to price mortality securities with normalized multivariate exponential titling based on the estimated mortality correlations and jump parameters. Our results show the significance of modeling mortality correlations and transient jumps in mortality security pricing.

Multi-population mortality models: A factor copula approach

“…14 7 Our selected countries and sample period are exactly the same as those used in Lin et al (2013). We follow the procedure as described in Lin et al (2013) to collect and compile mortality data for these six countries. We thank Yijia Lin for providing their mortality data for the purpose of comparison.…”

“…To derive the risk-neutral measure, we select the following seven mortality bond transactions as those used in Lin et al (2013): the Vita II bond (Tranches B, C and D), the Tartan bond (Tranche B) and the Osiris bond (Tranche B2, C and D). We summarize the issue size, date, maturity, coupon rate, attachment and detachment points, and index composition for these bonds in Table 9.…”

“…We believe this is problematic since Gaussian copulas lack tail dependence and are therefore inadequate to model the joint mortality events. Our approach is related to Lin et al (2013), but our model uses a two-stage multivariate analysis based on a factor copula approach which overcomes the problems noted here and has other advantages that we subsequently discuss.…”

“…This assumption might be justified by the long-term mortality comovements and so be applicable to longevity risk modeling, but it seems too strong to model the short-term mortality dependence. Lin et al (2013) develop a jump diffusion mortality model for multiple countries where mortality dependence comes from common jumps and the correlation between idiosyncratic risks. Their approach focuses on analyzing correlations among the raw mortality data but the raw data exhibit noise such as autocorrelation or volatility clustering that could possibly confound the dependence structure.…”

Forecasting mortality for small populations by mixing mortality data

“…Börger and Aleksic (2011) describe a multi-population projection model, assuming that the various groups share a common trend. Lin et al (2012) analyze mortality-linked securities with a model accounting for mortality correlations among countries, considering that the pay-off of such securities is based on three or more population mortality indexes. Plat (2009) discusses basis risk, relating the mortality of an insurance portfolio to the mortality of a national population.…”