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Level dependent annuities: Defaults of multiple degrees

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Author Info

  • Mjøs, Aksel

    ()
    (SNF - Institute for Research in Economics and Business Administration)

  • Persson, Svein-Arne

    ()
    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

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    Abstract

    Motivated by the risk of stopped debt coupon payments from a leveraged company in financial distress, we value a level dependent annuity contract where the annuity rate depends on the value of an underlying asset-process. The range of possible values of the asset is divided into a finite number of regions. The annuity rate is constant within each region, but may differ between the regions. We consider both in finite and finite annuities, with or without bankruptcy risk, i.e., bankruptcy occurs if the asset value process hits an absorbing boundary. Such annuities are common in models of debt with credit risk in financial economics. Suspension of debt service under the US Chapter 11 provisions is one well-known real-world example. We present closed-form formulas for the market value of such multi-level annuities contracts when the market value of the underlying asset is assumed to follow a geometric Brownian motion.

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    Bibliographic Info

    Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2008/6.

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    Length: 24 pages
    Date of creation: 12 Mar 2008
    Date of revision:
    Handle: RePEc:hhs:nhhfms:2008_006

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    Postal: NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
    Phone: +47 55 95 92 93
    Fax: +47 55 95 96 50
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    Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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    Keywords: Multi-level annuity; credit risk; financial distress;

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    References

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    1. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Broadie, Mark & Kaya, Özgür, 2007. "A Binomial Lattice Method for Pricing Corporate Debt and Modeling Chapter 11 Proceedings," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(02), pages 279-312, June.
    3. Mark Broadie & Mikhail Chernov & Suresh Sundaresan, 2007. "Optimal Debt and Equity Values in the Presence of Chapter 7 and Chapter 11," Journal of Finance, American Finance Association, vol. 62(3), pages 1341-1377, 06.
    4. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-67, May.
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