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Linear Credit Risk Models

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  • Damien Ackerer
  • Damir Filipovi'c

Abstract

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors. The price of a CDS option can be uniformly approximated by polynomials in the factors. Multi-name models can produce simultaneous defaults, generate positively as well as negatively correlated default intensities, and accommodate stochastic interest rates. A calibration study illustrates the versatility of these models by fitting CDS spread time series. A numerical analysis validates the efficiency of the option price approximation method.

Suggested Citation

  • Damien Ackerer & Damir Filipovi'c, 2016. "Linear Credit Risk Models," Papers 1605.07419, arXiv.org, revised Jan 2018.
  • Handle: RePEc:arx:papers:1605.07419
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    File URL: http://arxiv.org/pdf/1605.07419
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    References listed on IDEAS

    as
    1. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, vol. 176(2), pages 93-111.
    2. Corrado, Charles J & Su, Tie, 1996. "Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, Summer.
    3. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195.
    4. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31 World Scientific Publishing Co. Pte. Ltd..
    5. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    6. Farshid Jamshidian, 2004. "Valuation of credit default swaps and swaptions," Finance and Stochastics, Springer, vol. 8(3), pages 343-371, August.
    7. Tomasz Bielecki & Monique Jeanblanc & Marek Rutkowski, 2011. "Hedging of a credit default swaption in the CIR default intensity model," Finance and Stochastics, Springer, vol. 15(3), pages 541-572, September.
    8. Maximilian Ga{ss} & Kathrin Glau & Mirco Mahlstedt & Maximilian Mair, 2015. "Chebyshev Interpolation for Parametric Option Pricing," Papers 1505.04648, arXiv.org, revised Jul 2016.
    9. Jefferson Duarte, 2004. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 379-404.
    10. Damir Filipovi'c & Eberhard Mayerhofer & Paul Schneider, 2011. "Density Approximations for Multivariate Affine Jump-Diffusion Processes," Papers 1104.5326, arXiv.org, revised Oct 2011.
    11. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    12. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    13. Gourieroux, Christian & Jasiak, Joann, 2006. "Multivariate Jacobi process with application to smooth transitions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 475-505.
    14. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Mar 2018.
    15. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    16. Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2014. "Nonlinear Kalman Filtering in Affine Term Structure Models," Management Science, INFORMS, vol. 60(9), pages 2248-2268, September.
    17. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    18. Damiano Brigo & Aurélien Alfonsi, 2005. "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model," Finance and Stochastics, Springer, vol. 9(1), pages 29-42, January.
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    Cited by:

    1. Damien Ackerer & Thibault Vatter, 2016. "Dependent Defaults and Losses with Factor Copula Models," Papers 1610.03050, arXiv.org, revised Jan 2018.
    2. Damir Filipović & Martin Larsson, 2016. "Polynomial diffusions and applications in finance," Finance and Stochastics, Springer, vol. 20(4), pages 931-972, October.

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