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Precautionary Measures for Credit Risk Management in Jump Models

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  • Masahiko Egami
  • Kazutoshi Yamazaki
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    Abstract

    Sustaining efficiency and stability by properly controlling the equity to asset ratio is one of the most important and difficult challenges in bank management. Due to unexpected and abrupt decline of asset values, a bank must closely monitor its net worth as well as market conditions, and one of its important concerns is when to raise more capital so as not to violate capital adequacy requirements. In this paper, we model the tradeoff between avoiding costs of delay and premature capital raising, and solve the corresponding optimal stopping problem. In order to model defaults in a bank’s loan/credit business portfolios, we represent its net worth by appropriate L´evy processes, and solve explicitly for the double exponential jump diffusion process. In particular, for the spectrally negative case, we generalize the formulation using the scale function, and obtain explicitly the optimal solutions for the exponential jump diffusion process.

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    File URL: http://www.econ.kyoto-u.ac.jp/projectcenter/Paper/e-10-001.pdf
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    Bibliographic Info

    Paper provided by Graduate School of Economics Project Center, Kyoto University in its series Discussion papers with number e-10-001.

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    Length: 33 pages
    Date of creation: Apr 2010
    Date of revision:
    Handle: RePEc:kue:dpaper:e-10-001

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    Related research

    Keywords: Credit risk management; Double exponential jump diffusion; Spectrally negative Levy processes; Scale functions; Optimal stopping;

    References

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    1. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, INFORMS, vol. 50(9), pages 1178-1192, September.
    2. Nan Chen & S. G. Kou, 2009. "Credit Spreads, Optimal Capital Structure, And Implied Volatility With Endogenous Default And Jump Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 19(3), pages 343-378.
    3. Leland, Hayne E, 1994. " Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, American Finance Association, vol. 49(4), pages 1213-52, September.
    4. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, Springer, vol. 6(2), pages 237-263.
    5. Leland, Hayne E & Toft, Klaus Bjerre, 1996. " Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, American Finance Association, vol. 51(3), pages 987-1019, July.
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