Mortality Dependence and Longevity Bond Pricing: A Dynamic Factor Copula Mortality Model With the GAS Structure

Abstract

Modeling mortality dependence for multiple populations has significant implications for mortality/longevity risk management. A natural way to assess multivariate dependence is to use copula models. The application of copula models in the multipopulation mortality analysis, however, is still in its infancy. In this article, we present a dynamic multipopulation mortality model based on a two‐factor copula and capture the time‐varying dependence using the generalized autoregressive score (GAS) framework. Our model is simple and flexible in terms of model specification and is widely applicable to high dimension data. Using the Swiss Re Kortis longevity trend bond as an example, we use our model to estimate the probability distribution of principal reduction and some risk measures such as probability of first loss, conditional expected loss, and expected loss. Due to the similarity in the structure and design of CAT bonds and mortality/longevity bonds, we borrow CAT bond pricing techniques for mortality/longevity bond pricing. We find that our pricing model generates par spreads that are close to the actual spreads of previously issued mortality/longevity bonds.

Longevity risk and capital markets: the 2018–19 update

“…• Design and pricing of longevity bonds and other longevity-linked products (e.g. Blake et al, 2006aBlake et al, , 2006bBlake et al, , 2014Bauer, 2006;Bauer & Ruß, 2006;Antolin & Bloomestein, 2007;Bauer & Kramer, 2007Barbarin, 2008;Bauer et al, 2010b;Chen & Cummins, 2010;Kogure & Kurachi, 2010;Bravo, 2011;Dowd et al, 2011a;Mayhew & Smith, 2011;Zhou et al, 2011Zhou et al, , 2013Chen et al, 2013;Shen & Siu, 2013;Denuit et al, 2015;Hunt & Blake, 2015;Milevsky & Salisbury, 2015;Yang et al, 2015;Wang & Li, 2016;Chen et al, 2017;Lin et al, 2017b ;Leung et al, 2018;MacMinn & Richter, 2018;. • Design and pricing of longevity-linked derivatives (e.g.…”

Modelling Mortality Dependence With Regime-Switching Copulas

“…However, VECM only captures linear and symmetric dependence in time and between series, and therefore can be restrictive in a high-dimensional case where dependence structure is complex. Wang et al (2015), Chen et al (2015), Chuliá et al (2016) and Chen et al (2017) proposed the application of multivariate copulas to capture a wider range of mortality dependence. More specifically, to model mortality dependence Chen et al (2015) used a static one-factor copula in which the factor is common among all population groups.…”

“…Chuliá et al (2016) fitted generalized dynamic factor models to the differences of the log-mortality rates. Chen et al (2017) improved the work of Chen et al (2015) by adding a country-specific factor and allowing copula parameters to vary with time. Copula is a flexible tool for modelling high-dimensional dependence because it allows for the construction of a joint distribution by estimating marginal distributions and copula separately.…”

“…In the second step, we fit an ARIMA-GARCH model to each series of period effects in order to capture autocorrelation and conditional heteroscedasticity. Mortality heteroskedasticity has been detected and subsequently captured by GARCH model by several researchers, including Gao and Hu (2009), Chai et al (2013), Chen et al (2015), Lin et al (2015), Wang and Li (2016) and Chen et al (2017). In the second step, we model the dependence between the residuals series using copulas.…”

Using Multivariant Regression Analysis to Compute Longevity Risk and Actuarial Liability: The Case of Social Benefits for Workers in Venezuela

“…As pointed out by [4], the effort to model mortality dependence for multiple populations has important implications for mortality/longevity risk management. Their study presents a dynamic multi-population motality analysis using copula models to assess multivariate dependence.…”