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Indifference of Defaultable Bonds with Stochastic Intensity models

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  • Regis Houssou
  • Olivier Besson
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    Abstract

    The utility-based pricing of defaultable bonds in the case of stochastic intensity models of default risk is discussed. The Hamilton-Jacobi- Bellman (HJB) equations for the value functions is derived. A finite difference method is used to solve this problem. The yield-spreads for both buyer and seller are extracted. The behaviour of the spread curve given the default intensity is analyzed. Finally the impacts of the risk aversion and the correlation coefficient are discussed.

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    File URL: http://arxiv.org/pdf/1003.4118
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    Paper provided by arXiv.org in its series Papers with number 1003.4118.

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    Date of creation: Mar 2010
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    Handle: RePEc:arx:papers:1003.4118

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    1. Darrell Duffie & Thaleia Zariphopoulou, 1993. "Optimal Investment With Undiversifiable Income Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 3(2), pages 135-148.
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    7. Jarrow, Robert A & Lando, David & Turnbull, Stuart M, 1997. "A Markov Model for the Term Structure of Credit Risk Spreads," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 10(2), pages 481-523.
    8. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
    9. Sennewald, Ken, 2007. "Controlled stochastic differential equations under Poisson uncertainty and with unbounded utility," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 31(4), pages 1106-1131, April.
    10. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, American Finance Association, vol. 31(2), pages 351-67, May.
    11. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 10(1), pages 39-52.
    12. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers, Massachusetts Institute of Technology (MIT), Sloan School of Management 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    13. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, American Finance Association, vol. 50(1), pages 53-85, March.
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