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Systematic equity-based credit risk: A CEV model with jump to default

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  • Campi, Luciano
  • Polbennikov, Simon
  • Sbuelz, Alessandro
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    Abstract

    We use equity as the traded primitive for a detailed analysis of systematic default risk. Default is parsimoniously represented by equity value hitting the zero barrier so that, unlike in reduced-form models, the explicit linkage to the firm's capital structure is preserved, but, unlike in structural models, restrictive assumptions on the structure are avoided. Default risk is either jump-like or diffusive. The equity price can jump to default. In line with recent empirical evidence on the jump-to-default risk price, we highlight how reasonable choices of the pricing kernel can imply remarkable differences in the equity-price-dependent status between the objective default intensity and the risk-neutral intensity. As equity returns experience negative diffusive shocks, their CEV-type local variance increases and boosts the objective and risk-neutral probabilities of diffusive default. A parsimonious version of our general model simultaneously enables analytical credit-risk management and analytical pricing of credit-sensitive instruments. Easy cross-asset hedging ensues.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 33 (2009)
    Issue (Month): 1 (January)
    Pages: 93-108

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    Handle: RePEc:eee:dyncon:v:33:y:2009:i:1:p:93-108

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    Web page: http://www.elsevier.com/locate/jedc

    Related research

    Keywords: Market price of credit risk Constant-elasticity-of-variance (CEV) diffusive risk Jump-to-default risk Equity Corporate bonds Credit default swaps;

    References

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    Cited by:
    1. Bazdresch, Santiago, 2013. "The role of non-convex costs in firms' investment and financial dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 929-950.
    2. Bao, Qunfang & Li, Shenghong & Gong, Donggeng, 2012. "Pricing VXX option with default risk and positive volatility skew," European Journal of Operational Research, Elsevier, vol. 223(1), pages 246-255.
    3. Rafael Mendoza-Arriaga & Vadim Linetsky, 2011. "Pricing equity default swaps under the jump-to-default extended CEV model," Finance and Stochastics, Springer, vol. 15(3), pages 513-540, September.
    4. Azizpour, Shahriar & Giesecke, Kay & Kim, Baeho, 2011. "Premia for correlated default risk," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1340-1357, August.
    5. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2013. "Shapes of implied volatility with positive mass at zero," Papers 1310.1020, arXiv.org.
    6. Claudio Fontana & Juan Miguel A. Montes, 2012. "A unified approach to pricing and risk management of equity and credit risk," Papers 1212.5395, arXiv.org, revised May 2013.

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