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The study of dynamics for credit default risk by backward stochastic differential equation method

Author

Listed:
  • Kun Tian

    (Department of Stats & Maths, Shanghai Lixin University of Accounting & Finance, Shanghai 201620, P. R. China)

  • Dewen Xiong

    (#x2020;Department of Maths, Shanghai JiaoTong University, Shanghai 200240, P. R. China)

  • Wenchao Yan

    (#x2020;Department of Maths, Shanghai JiaoTong University, Shanghai 200240, P. R. China)

  • George Xianzhi Yuan

    (#x2021;Guiyang Institute for Bigdata & Finance, Guizhou University of Finance & Economics, Guiyang 550025, P. R. China§School of Financial Technology, Shanghai Lixin University of Accounting & Finance, Shanghai 201209, P. R. China¶Center for Financial Engineering, Soochow University, Suzhou 215008, P. R. China∥Business School & Advanced Institute of Finance, Sun Yat-Sen University, Guangzhou 510275, P. R. China)

Abstract

In this paper, we discuss the dynamics of credit default risk for bilateral collateralized credit valuation adjusted (BCCVA) for counterparty credit risk with two positive collateral accounts by assuming default times for both investor and counterparty satisfying the density hypothesis, and the contagion risk between them being reflected by the density process. We first split the price process into three key parts, and then describe the dynamics of each part by using backward stochastic differential equations (BSDEs). As applications, we introduce the “double” Cox model, in which the BSDEs have their specific forms and thus results in this paper generalize and improve corresponding theoretic results in the existing literature. We also would like to point out that, in this paper, we do not pay attention to explore how the introduction of default contagion impacts with true market data for the BCCVA predicted by for a model without contagion versus a model with contagion, but will plan to conduct the study on the impact for BCCVA with or without contagion in a separate research project.

Suggested Citation

  • Kun Tian & Dewen Xiong & Wenchao Yan & George Xianzhi Yuan, 2018. "The study of dynamics for credit default risk by backward stochastic differential equation method," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 1-32, December.
    • Handle: RePEc:wsi:ijfexx:v:05:y:2018:i:04:n:s242478631850038x
    DOI: 10.1142/S242478631850038X
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    References listed on IDEAS

    as
    1. Ying Jiao, 2009. "Multiple defaults and contagion risks," Papers 0912.3132, arXiv.org.
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