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A General Framework For Pricing Credit Risk

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  • Alain BÉlanger
  • Steven E. Shreve
  • Dennis Wong

Abstract

A framework is provided for pricing derivatives on defaultable bonds and other credit‐risky contingent claims. The framework is in the spirit of reduced‐form models, but extends these models to include the case that default can occur only at specific times, such as coupon payment dates. Although the framework does not provide an efficient setting for obtaining results about structural models, it is sufficiently general to include most structural models, and thereby highlights the commonality between reduced‐form and structural models. Within the general framework, multiple recovery conventions for contingent claims are considered: recovery of a fraction of par, recovery of a fraction of a no‐default version of the same claim, and recovery of a fraction of the pre‐default value of the claim. A stochastic‐integral representation for credit‐risky contingent claims is provided, and the integrand for the credit exposure part of this representation is identified. In the case of intensity‐based, reduced‐form models, credit spread and credit‐risky term structure are studied.

Suggested Citation

  • Alain BÉlanger & Steven E. Shreve & Dennis Wong, 2004. "A General Framework For Pricing Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 317-350, July.
    • Handle: RePEc:bla:mathfi:v:14:y:2004:i:3:p:317-350
    DOI: 10.1111/j.0960-1627.2004.t01-1-00193.x
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    Citations

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    Cited by:

    1. Agostino Capponi & José Figueroa-López & Andrea Pascucci, 2015. "Dynamic credit investment in partially observed markets," Finance and Stochastics, Springer, vol. 19(4), pages 891-939, October.
    2. Martin Keller-Ressel & Thorsten Schmidt & Robert Wardenga, 2018. "Affine processes beyond stochastic continuity," Papers 1804.07556, arXiv.org, revised Dec 2018.
    3. Lijun Bo & Xindan Li & Yongjin Wang & Xuewei Yang, 2013. "Optimal Investment and Consumption with Default Risk: HARA Utility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(3), pages 261-281, September.
    4. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2015. "Arbitrage-Free Pricing of XVA -- Part I: Framework and Explicit Examples," Papers 1501.05893, arXiv.org, revised Aug 2016.
    5. Agostino Capponi & Lijun Bo, 2016. "Robust Optimization of Credit Portfolios," Papers 1603.08169, arXiv.org.
    6. Tolulope Fadina & Thorsten Schmidt, 2019. "Default Ambiguity," Risks, MDPI, vol. 7(2), pages 1-17, June.
    7. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2016. "Arbitrage-Free XVA," Papers 1608.02690, arXiv.org.
    8. Xin Guo & Robert A. Jarrow & Yan Zeng, 2009. "Credit Risk Models with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 320-332, May.
    9. Fontana, Claudio & Schmidt, Thorsten, 2018. "General dynamic term structures under default risk," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3353-3386.
    10. Lijun Bo & Agostino Capponi, 2017. "Optimal Credit Investment with Borrowing Costs," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 546-575, May.
    11. Kau, James B. & Keenan, Donald C. & Lyubimov, Constantine & Carlos Slawson, V., 2011. "Subprime mortgage default," Journal of Urban Economics, Elsevier, vol. 70(2), pages 75-87.
    12. Tahir Choulli & Catherine Daveloose & Michèle Vanmaele, 2020. "A martingale representation theorem and valuation of defaultable securities," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1527-1564, October.
    13. Damiano Brigo & Agostino Capponi & Andrea Pallavicini, 2014. "Arbitrage-Free Bilateral Counterparty Risk Valuation Under Collateralization And Application To Credit Default Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 125-146, January.
    14. T. Choulli & S. Alsheyab, 2024. "Linear reflected backward stochastic differential equations arising from vulnerable claims in markets with random horizon," Papers 2408.04758, arXiv.org.
    15. Tahir Choulli & Emmanuel Lepinette, 2024. "Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon," Papers 2401.05713, arXiv.org.
    16. Agostino Capponi & Stefano Pagliarani & Tiziano Vargiolu, 2014. "Pricing vulnerable claims in a Lévy-driven model," Finance and Stochastics, Springer, vol. 18(4), pages 755-789, October.
    17. Lijun Bo & Agostino Capponi, 2014. "Bilateral credit valuation adjustment for large credit derivatives portfolios," Finance and Stochastics, Springer, vol. 18(2), pages 431-482, April.
    18. Tahir Choulli & Ferdoos Alharbi, 2022. "Representation for martingales living after a random time with applications," Papers 2203.11072, arXiv.org, revised Nov 2022.
    19. Frank Gehmlich & Thorsten Schmidt, 2015. "A generalized intensity based framework for single-name credit risk," Papers 1512.03896, arXiv.org.
    20. Claudio Fontana & Thorsten Schmidt, 2016. "General dynamic term structures under default risk," Papers 1603.03198, arXiv.org, revised Nov 2017.
    21. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    22. Lijun Bo & Shihua Wang & Xiang Yu, 2021. "Mean Field Game of Optimal Relative Investment with Jump Risk," Papers 2108.00799, arXiv.org, revised Feb 2023.
    23. Sandrine Gumbel & Thorsten Schmidt, 2021. "Defaultable term structures driven by semimartingales," Papers 2103.01577, arXiv.org, revised Aug 2021.
    24. Lijun Bo & Agostino Capponi, 2017. "Robust Optimization of Credit Portfolios," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 30-56, January.
    25. Frank Gehmlich & Thorsten Schmidt, 2014. "Dynamic Defaultable Term Structure Modelling beyond the Intensity Paradigm," Papers 1411.4851, arXiv.org, revised Jul 2015.

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