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PDE approach to valuation and hedging of credit derivatives

Author

Listed:
  • Tomasz Bielecki
  • Monique Jeanblanc
  • Marek Rutkowski

Abstract

This paper presents a PDE approach in a Markovian setting to hedge defaultable derivatives. The arbitrage price and the hedging strategy for an attainable contingent claim are described in terms of solutions of a pair of coupled PDEs. For some standard examples of defaultable claims, we provide explicit formulae for prices and hedging strategies.

Suggested Citation

  • Tomasz Bielecki & Monique Jeanblanc & Marek Rutkowski, 2005. "PDE approach to valuation and hedging of credit derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 257-270.
    • Handle: RePEc:taf:quantf:v:5:y:2005:i:3:p:257-270
    DOI: 10.1080/14697680500149297
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    Citations

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    Cited by:

    1. A. Itkin & V. Shcherbakov & A. Veygman, 2019. "New Model For Pricing Quanto Credit Default Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-37, May.
    2. Damiano Brigo & Nicola Pede & Andrea Petrelli, 2019. "Multi-Currency Credit Default Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-35, June.
    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. Akira Kashiwabara & Nobuhiro Nakamura, 2011. "Dynamic Investment Strategies to Reaction–Diffusion Systems Based upon Stochastic Differential Utilities," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(2), pages 131-150, May.
    5. Nan Chen & S. G. Kou, 2009. "Credit Spreads, Optimal Capital Structure, And Implied Volatility With Endogenous Default And Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 343-378, July.
    6. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2022. "Nonlinear Valuation with XVAs: Two Converging Approaches," Mathematics, MDPI, vol. 10(5), pages 1-31, March.
    7. Andrey Itkin & Fazlollah Soleymani, 2019. "Four-factor model of Quanto CDS with jumps-at-default and stochastic recovery," Papers 1912.08713, arXiv.org.
    8. Li, Shaoyu & Huang, Henry H. & Zhang, Teng, 2020. "Generalized affine transform on pricing quanto range accrual note," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    9. Jin Liang & Jun Ma & Tao Wang & Qin Ji, 2011. "Valuation of Portfolio Credit Derivatives with Default Intensities Using the Vasicek Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(1), pages 33-54, March.
    10. Jun Sekine & Akihiro Tanaka, 2020. "Notes on Backward Stochastic Differential Equations for Computing XVA," Papers 2006.02173, arXiv.org.
    11. Damiano Brigo & Nicola Pede & Andrea Petrelli, 2015. "Multi Currency Credit Default Swaps Quanto effects and FX devaluation jumps," Papers 1512.07256, arXiv.org, revised Jan 2018.
    12. A. Itkin & V. Shcherbakov & A. Veygman, 2017. "Influence of jump-at-default in IR and FX on Quanto CDS prices," Papers 1711.07133, arXiv.org.
    13. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2018. "Risk-neutral valuation under differential funding costs, defaults and collateralization," Papers 1802.10228, arXiv.org.
    14. Damiano Brigo & Cristin Buescu & Marek Rutkowski, 2016. "Funding, repo and credit inclusive valuation as modified option pricing," Papers 1602.05998, arXiv.org, revised Jun 2017.

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