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Evaluation of credit value adjustment in K-forward

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  • Hao, Xuemiao
  • Liang, Chunli
  • Wei, Linghua

Abstract

We model and quantify counterparty credit risk for K-forward, a newly proposed longevity-linked security. We focus on the evaluation of credit value adjustment (CVA) from the longevity risk hedger’s perspective. The modelling involves two folds. First, we use a vector autoregressive integrated moving-average process to model the time series of mortality indexes that is obtained by applying the original Cairns–Blake–Dowd model. Then, the risk-neutral default probability of the hedge provider is obtained by calibrating a reduced-form default model on the market price of bonds issued by the hedge provider. We calculate and compare CVA in K-forwards for different combinations of hedger provider, reference year and recovery rate.

Suggested Citation

  • Hao, Xuemiao & Liang, Chunli & Wei, Linghua, 2017. "Evaluation of credit value adjustment in K-forward," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 95-103.
    • Handle: RePEc:eee:insuma:v:76:y:2017:i:c:p:95-103
    DOI: 10.1016/j.insmatheco.2017.07.004
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    References listed on IDEAS

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    1. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2011. "Mortality density forecasts: An analysis of six stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 355-367, May.
    2. Wai-Sum Chan & Johnny Li & Jackie Li, 2014. "The CBD Mortality Indexes: Modeling and Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 38-58.
    3. Enrico Biffis & David Blake & Lorenzo Pitotti & Ariel Sun, 2016. "The Cost of Counterparty Risk and Collateralization in Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(2), pages 387-419, June.
    4. Duan, Jin-Chuan & Sun, Jie & Wang, Tao, 2012. "Multiperiod corporate default prediction—A forward intensity approach," Journal of Econometrics, Elsevier, vol. 170(1), pages 191-209.
    5. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    6. Tan, Chong It & Li, Jackie & Li, Johnny Siu-Hang & Balasooriya, Uditha, 2014. "Parametric mortality indexes: From index construction to hedging strategies," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 285-299.
    7. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    8. Samuel Cox & Hal Pedersen, 2000. "Catastrophe Risk Bonds," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 56-82.
    9. Kevin Dowd & Andrew Cairns & David Blake & Guy Coughlan & David Epstein & Marwa Khalaf-Allah, 2010. "Backtesting Stochastic Mortality Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(3), pages 281-298.
    10. Blake, D. & Cairns, A. J. G. & Dowd, K., 2006. "Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities," British Actuarial Journal, Cambridge University Press, vol. 12(1), pages 153-197, March.
    11. Andrew J.G. Cairns & Kevin Dowd & David Blake & Guy D. Coughlan, 2014. "Longevity hedge effectiveness: a decomposition," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 217-235, February.
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    13. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
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    Cited by:

    1. Kenneth Q. Zhou & Johnny S.-H. Li & Pintao Lyu, 2024. "Bringing parametric mortality indexes to practice: a generalized CBD model with stochastic socioeconomic differentials in mortality improvements," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 49(2), pages 295-319, April.

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    More about this item

    Keywords

    Credit value adjustment; K-forward; Longevity risk; Multivariate time series; Risk-neutral default probability;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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