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Level dependent annuities: Defaults of multiple degrees

Author

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  • 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)

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.

Suggested Citation

  • Mjøs, Aksel & Persson, Svein-Arne, 2008. "Level dependent annuities: Defaults of multiple degrees," Discussion Papers 2008/6, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2008_006
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    File URL: http://hdl.handle.net/11250/163926
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    References listed on IDEAS

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    1. 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 351-367, May.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    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, June.
    4. 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.
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    More about this item

    Keywords

    Multi-level annuity; credit risk; financial distress;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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