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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

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.

Suggested Citation

  • Campi, Luciano & Polbennikov, Simon & Sbuelz, Alessandro, 2009. "Systematic equity-based credit risk: A CEV model with jump to default," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 93-108, January.
  • Handle: RePEc:eee:dyncon:v:33:y:2009:i:1:p:93-108
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    Cited by:

    1. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2015. "Pricing and static hedging of American-style knock-in options on defaultable stocks," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 343-360.
    2. 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.
    3. 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.
    4. Axel A. Araneda, 2022. "Credit Default Swaps and the mixed-fractional CEV model," Papers 2211.07564, arXiv.org.
    5. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2013. "Shapes of implied volatility with positive mass at zero," Papers 1310.1020, arXiv.org, revised May 2017.
    6. Ruxing Xu & Dan Wu & Ronghua Yi, 2016. "Pricing Cdss And Cds Options Under A Regime-Switching Cev Process With Jump To Default," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(1), pages 253-271.
    7. Dean Fantazzini & Stephan Zimin, 2020. "A multivariate approach for the simultaneous modelling of market risk and credit risk for cryptocurrencies," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 47(1), pages 19-69, March.
    8. Fontana, Claudio & Schmidt, Thorsten, 2018. "General dynamic term structures under default risk," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3353-3386.
    9. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2017. "Shapes of implied volatility with positive mass at zero," Working Papers 2017-77, Center for Research in Economics and Statistics.
    10. 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.
    11. Jiang, Yixiao, 2022. "Credit ratings, financial ratios, and equity risk: A decomposition analysis based on Moody’s, Standard & Poor’s and Fitch’s ratings," Finance Research Letters, Elsevier, vol. 46(PB).
    12. Feixue Huang & Yan He, 2010. "Enactment of Default Point in KMV Model on CMBC, SPDB, CMB, Huaxia Bank and SDB," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 1(1), pages 30-36, December.
    13. 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.
    14. 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.
    15. Ying Jiao & Idris Kharroubi, 2016. "Information uncertainty related to marked random times and optimal investment," Papers 1607.02743, arXiv.org, revised Mar 2017.
    16. Sakurai, Yuji & Uchida, Yoshihiko, 2014. "Rehypothecation dilemma: Impact of collateral rehypothecation on derivative prices under bilateral counterparty credit risk," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 361-373.

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