Mortality Modeling With Non‐Gaussian Innovations and Applications to the Valuation of Longevity Swaps

Self Cite

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.

“…(), Dowd et al. (), and Wang, Huang, and Liu (). We consider a survival index for a cohort of

x_{0} = 65

, which follows the framework of Wang, Yang, and Huang (), with the underlying survivor index based on multi‐population survivor distributions in order to reduce basis risk .…”

Section: Multicountry Survivor Index Swapsmentioning

confidence: 99%

Section: Multicountry Survivor Index Swapsmentioning

confidence: 99%

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

Zhu¹,

Tan²,

Wang³

2017

Self Cite

“…In addition, some articles have focused on comparing existing models in the literature (e.g., Stallard, ). Another strand of the literature is using well‐known techniques from econometrics or other disciplines to model multipopulation mortality (e.g., Hatzopoulos and Haberman, ; Lin, Liu, and Yu, ; Wang, Huang, and Liu, ; Yang and Wang, ; Zhou et al, ).…”

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.

“…Using this approach, Dowd et al. (), Wang and Yang (), and Wang, Huang, and Liu () find proportional markups varying from close to 0 to around 5 percent.…”

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confidence: 99%

“…m(s, x + s, k): the crude death rate for cohort(x, k) in the period [s, s + 1), that is, the number of deaths in cohort (x, k) in the period [s, s + 1) divided by the exposure to 8 Due to market incompleteness, the existing literature on longevity risk management typically considers model-based risk premiums, for example, proportional markups inferred from the Wang transform. Using this approach,Dowd et al (2006),Wang and Yang (2013),and Wang, Huang, and Liu (2013)find proportional markups varying from close to 0 to around 5 percent. death, which is defined as the number of person years of cohort (x, k) in the period [s, s + 1); r q(s, x + s, k): the probability (determined at time s + 1) that an individual belonging to cohort (x, k) who is still alive at time s (and hence aged x + s), dies before time s + 1.…”

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confidence: 99%

Robust Mean–Variance Hedging of Longevity Risk

Waegenaere²,

Melenberg

2017

Parameter uncertainty and model misspecification can have a significant impact on the performance of hedging strategies for longevity risk. To mitigate this lack of robustness, we propose an approach in which the optimal hedge is determined by optimizing the worst‐case value of the objective function with respect to a set of plausible probability distributions. In the empirical analysis, we consider an insurer who hedges longevity risk using a longevity bond, and we compare the worst‐case (robust) optimal hedges with the classical optimal hedges in which parameter uncertainty and model misspecification are ignored. We find that unless the risk premium on the bond is close to zero, the robust optimal hedge is significantly less sensitive to variations in the underlying probability distribution. Moreover, the robust optimal hedge on average outperforms the nominal optimal hedge unless the probability distribution used by the nominal hedger is close to the true distribution.