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The cost of counterparty risk and collateralization in longevity swaps

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  • Biffis, Enrico
  • Blake, David
  • Pitotti, Lorenzo
  • Sun, Ariel

Abstract

Derivative longevity risk solutions, such as bespoke and indexed longevity swaps, allow pension schemes and annuity providers to swap out longevity risk, but introduce counterparty credit risk, which can be mitigated if not fully eliminated by collateralization. We examine the impact of bilateral default risk and collateral rules on the marking to market of longevity swaps, and show how longevity swap rates must be determined endogenously from the collateral flows associated with the marking-to-market procedure. For typical interest rate and mortality parameters, we find that the impact of collateralization is modest in the presence of symmetric default risk, but more pronounced when default risk and/or collateral rules are asymmetric. Our results suggest that the overall cost of collateralization is comparable with, and often much smaller than, that found in the interest-rate swaps market (as a result of the offsetting effects of interest rate and longevity risks), which may then provide the appropriate reference framework for the credit enhancement of both indemnity-based and indexed longevity risk solutions.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 35740.

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Date of creation: 20 Jun 2011
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Handle: RePEc:pra:mprapa:35740

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Keywords: longevity swap; counterparty risk; default risk; collateral; marking-to-market;

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References

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  1. Dowd, Kevin & Cairns, Andrew J.G. & Blake, David & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2010. "Evaluating the goodness of fit of stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 255-265, December.
  2. Chen, Hua & Cummins, J. David, 2010. "Longevity bond premiums: The extreme value approach and risk cubic pricing," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 150-161, February.
  3. Damiano Brigo & Agostino Capponi, 2008. "Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps," Papers 0812.3705, arXiv.org, revised Nov 2009.
  4. Anna Rita Bacinello & Enrico Biffis & Pietro Millossovich, 2010. "Regression-based algorithms for life insurance contracts with surrender guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 1077-1090.
  5. Michael Johannes & Suresh Sundaresan, 2007. "The Impact of Collateralization on Swap Rates," Journal of Finance, American Finance Association, vol. 62(1), pages 383-410, 02.
  6. Cox, Samuel H. & Lin, Yijia & Pedersen, Hal, 2010. "Mortality risk modeling: Applications to insurance securitization," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 242-253, February.
  7. Anja De Waegenaere & Bertrand Melenberg & Ralph Stevens, 2010. "Longevity Risk," De Economist, Springer, vol. 158(2), pages 151-192, June.
  8. Kevin Dowd & David Blake & Andrew J. G. Cairns & Paul Dawson, 2006. "Survivor Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 1-17.
  9. Ludkovski, Michael & Young, Virginia R., 2008. "Indifference pricing of pure endowments and life annuities under stochastic hazard and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 14-30, February.
  10. J. David Cummins & Philippe Trainar, 2009. "Securitization, Insurance, and Reinsurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 463-492.
  11. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272, September.
  12. Duffie, Darrell & Huang, Ming, 1996. " Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-49, July.
  13. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
  14. Darius Lakdawalla & George Zanjani, 2006. "Catastrophe Bonds, Reinsurance, and the Optimal Collateralization of Risk-Transfer," NBER Working Papers 12742, National Bureau of Economic Research, Inc.
  15. 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.
  16. Biffis, Enrico & Blake, David, 2010. "Securitizing and tranching longevity exposures," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 186-197, February.
  17. Damiano Brigo & Agostino Capponi & Andrea Pallavicini & Vasileios Papatheodorou, 2011. "Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment including Re-Hypotecation and Netting," Papers 1101.3926, arXiv.org.
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Citations

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Cited by:
  1. Damiano Brigo, 2011. "Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin Lending," Papers 1111.1331, arXiv.org, revised Jun 2012.
  2. Meyricke, Ramona & Sherris, Michael, 2014. "Longevity risk, cost of capital and hedging for life insurers under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 147-155.

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