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

Journal of Risk and Insurance, 84: 393-415, 2017

24 Pages Posted: 6 Feb 2017 Last revised: 7 Jun 2017

See all articles by Hua Chen

Hua Chen

University of Hawaiʻi at Mānoa

Richard D. MacMinn

National Chengchi University; The University of Texas

Tao Sun

Lingnan University

Multiple version iconThere are 2 versions of this paper

Date Written: January 31, 2017

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 multi-population mortality analysis, however, is still in its infancy. In this paper, we present a dynamic multi-population 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.

Keywords: Multi-population mortality model, factor copulas, generalized autoregressive score models, the Kortis bond

Suggested Citation

Chen, Hua and MacMinn, Richard D. and Sun, Tao, Mortality Dependence and Longevity Bond Pricing: A Dynamic Factor Copula Mortality Model with the GAS Structure (January 31, 2017). Journal of Risk and Insurance, 84: 393-415, 2017. Available at SSRN: https://ssrn.com/abstract=2909244

Hua Chen (Contact Author)

University of Hawaiʻi at Mānoa ( email )

2404 Maile Way, E-602e
Honolulu, HI 96822
United States
(808) 956-8063 (Phone)
(808) 956-9887 (Fax)

Richard D. MacMinn

National Chengchi University ( email )

Taipei
Taiwan

The University of Texas ( email )

2317 Speedway
Austin, TX 78712
United States

Tao Sun

Lingnan University ( email )

8 Castle Peak Road
Lingnan University
Hong Kong, New Territories
China

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