Multi-Population Mortality Models: A Factor Copula Approach

This article proposes a new copula model known as the Lévy subordinated hierarchical Archimedean copulas (LSHAC) for multicountry mortality dependence modeling. To the best of our knowledge, this is the first article to apply the LSHAC model to mortality studies. Through an extensive empirical analysis on modeling mortality experiences of 13 countries, we demonstrate that the LSHAC model, which has the advantage of capturing the geographical structure of mortality data, yields better fit, compared to the elliptical copulas. In addition, the proposed LSHAC model generates out‐of‐sample forecasts with smaller standard deviations, when compared to other benchmark copula models. The LSHAC model also confirms that there is an association between geographical locations and dependence of the overall mortality improvement. These results yield new insights into future longevity risk management. Finally, the model is used to price a hypothetical survival index swap written on a weighted mortality index. The results highlight the importance of dependence modeling in managing longevity risk and reducing population basis risk.

“…We examine the best JO‐LSHAC model (Table ). For competing models, in addition to the Student's t copula, we also consider the factor copula model proposed by Chen, MacMinn, and Sun ()…”

Section: Multicountry Survivor Index Swapsmentioning

confidence: 99%

“…). Chen, MacMinn, and Sun () introduce factor copula into multipopulation mortality modeling. They employ a two‐stage procedure based on the time series analysis and a factor copula approach.…”

Section: Introductionmentioning

confidence: 99%

Modeling Multicountry Longevity Risk With Mortality Dependence: A Lévy Subordinated Hierarchical Archimedean Copulas Approach

Zhu¹,

Tan²,

Wang³

2017

“…A strand of the literature that examines multipopulation mortality that models primarily short‐term (instead of long‐term) relations starts with Li and Lee () where a common country‐specific trend is modeled using autoregressive processes. Other examples include but are not limited to Chen, MacMinn, and Sun () who apply a factor‐copula approach on different countries’ mortality data after they have been treated with time series models focusing on short‐term relations. We differ by using a Granger‐causality framework to identify short‐term relations among countries.…”

Section: Related Literature and Hypothesis Developmentmentioning

confidence: 99%

“…The academic literature on multipopulation mortality risk is relatively new and focuses almost entirely on non‐APAC countries. Most research has focused on developing models and improving existing models to capture the joint dynamics of at least two populations (e.g., Li and Lee, ; Cairns et al, ; Dowd et al, ; Li and Hardy, ; O'Hare and Li, ; Zhou et al, ; Chuang and Brockett, ; Chen, MacMinn, and Sun, ). In addition, some articles have focused on comparing existing models in the literature (e.g., Stallard, ).…”

Section: Introductionmentioning

confidence: 99%

Mortality Leads and Lags

Milidonis¹,

Efthymiou²

2016

Mortality risk varies geographically, especially in the Asia‐Pacific (APAC) region, where economic development is quite diverse. We present a newly collected data set on aggregate population mortality from 11 countries in APAC, which we rank based on their economic development. Using lead–lag analysis, we identify short‐term predictability in mortality risk across countries. Mortality improvements seem to appear faster in more developed than less developed countries. Such predictability is useful for longevity risk financing and in producing cross‐country mortality indices. We propose ways in which our results can benefit institutions manage their exposure in APAC mortality and longevity risk.

“…Many innovative products, such as mortality/longevity bonds, longevity swaps, buy‐ins, and buy‐outs, have been adopted (Tan, Blake, and MacMinn, ). A better understanding of the correlation among mortality improvements for multiple populations appears to be critical for issuers, investors, insurers, pension plans, and governments for several reasons (Cairns et al, ; Chen, MacMinn, and Sun, ). First, almost all mortality/longevity bonds are written on a weighted index based on the mortality experience of multiple populations.…”

Section: Introductionmentioning

confidence: 99%

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

Chen

MacMinn

Sun

2017

Self Cite

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.