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Correlated intensity, counter party risks, and dependent mortalities

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  • Ma, Jin
  • Yun, Youngyun

Abstract

In this paper we use an intensity-based framework to analyze and compute the correlated default probabilities, both in finance and actuarial sciences, following the idea of "change of measure" initiated by Collin-Dufresne et al. (2004). Our method is based on a representation theorem for joint survival probability among an arbitrary number of defaults, which works particularly effectively for certain types of correlated default models, including the counter-party risk models of Jarrow and Yu (2001) and related problems such as the phenomenon of "flight to quality". The results are also useful in studying the recently observed dependent mortality for married couples involving spousal bereavement. In particular we study in details a problem of pricing Universal Variable Life (UVL) insurance products. The explicit formulae for the joint-life status and last-survivor status (or equivalently, the probability distribution of first-to-default and last-to-default in a multi-firm setting) enable us to derive the explicit solution to the indifference pricing formula without using any advanced results in partial differential equations.

Suggested Citation

  • Ma, Jin & Yun, Youngyun, 2010. "Correlated intensity, counter party risks, and dependent mortalities," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 337-351, December.
    • Handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:337-351
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    References listed on IDEAS

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    1. Fan Yu, 2007. "Correlated Defaults In Intensity‐Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173, April.
    2. 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.
    3. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, vol. 72(5), pages 1377-1407, September.
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    5. Virginia Young, 2003. "Equity-Indexed Life Insurance: Pricing and Reserving Using the Principle of Equivalent Utility," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(1), pages 68-86.
    6. Yuanreng Hu & Noreen Goldman, 1990. "Mortality Differentials by Marital Status: An International Comparison," Demography, Springer;Population Association of America (PAA), vol. 27(2), pages 233-250, May.
    7. Tapani Valkonen & Pekka Martikainen & Jenni Blomgren, 2004. "Increasing excess mortality among non-married elderly people in developed countries," Demographic Research Special Collections, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 2(12), pages 305-330.
    8. Tomasz R. Bielecki & Monique Jeanblanc & Marek Rutkowski, 2006. "Hedging of Credit Derivatives in Models with Totally Unexpected Default," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 2, pages 35-100, World Scientific Publishing Co. Pte. Ltd..
    9. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

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    2. Yinghui Dong & Kam C. Yuen & Guojing Wang & Chongfeng Wu, 2016. "A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 459-486, June.

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