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Pricing credit default swaps with bilateral value adjustments

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  • Alexander Lipton
  • Ioana Savescu

Abstract

The paper studies the problem of computing adjustments for bilateral counterparty risk for a standard CDS in a three-factor first-passage time default risk model. Extending the existing literature that gives analytical expression for the transition probability density function (or Green's function) for two-dimensional Brownian motions absorbed at the boundaries in the positive quadrant, this paper gives a semi-analytical expression for Green's function for three-dimensional Brownian motions absorbed at first exit time from the positive octant. This is done by separating the problem into a radial and an angular part, of which the latter is universal and depends only on the correlation matrix. These mathematical results are then used to provide semi-analytical expressions for bilateral CVA/DVA of a credit default swap. An example of market data is analysed in detail and it is shown that these value adjustments can be surprisingly large.

Suggested Citation

  • Alexander Lipton & Ioana Savescu, 2014. "Pricing credit default swaps with bilateral value adjustments," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 171-188, January.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:1:p:171-188
    DOI: 10.1080/14697688.2013.828239
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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. Alexander Lipton, 2015. "Modern Monetary Circuit Theory, Stability of Interconnected Banking Network, and Balance Sheet Optimization for Individual Banks," Papers 1510.07608, arXiv.org.
    3. Andrey Itkin & Alexander Lipton, 2017. "Structural default model with mutual obligations," Review of Derivatives Research, Springer, vol. 20(1), pages 15-46, April.
    4. Vadim Kaushansky & Alexander Lipton & Christoph Reisinger, 2016. "Numerical analysis of an extended structural default model with mutual liabilities and jump risk," Papers 1701.00030, arXiv.org.
    5. Jie Chen & Liaoyuan Fan & Lingfei Li & Gongqiu Zhang, 2022. "A multidimensional Hilbert transform approach for barrier option pricing and survival probability calculation," Review of Derivatives Research, Springer, vol. 25(2), pages 189-232, July.
    6. Andrey Itkin & Fazlollah Soleymani, 2019. "Four-factor model of Quanto CDS with jumps-at-default and stochastic recovery," Papers 1912.08713, arXiv.org.
    7. Alexander Lipton, 2016. "Modern Monetary Circuit Theory, Stability Of Interconnected Banking Network, And Balance Sheet Optimization For Individual Banks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-57, September.
    8. Andrey Itkin & Alexander Lipton, 2014. "Efficient solution of structural default models with correlated jumps and mutual obligations," Papers 1408.6513, arXiv.org, revised Nov 2014.
    9. Vadim Kaushansky & Alexander Lipton & Christoph Reisinger, 2017. "Transition probability of Brownian motion in the octant and its application to default modeling," Papers 1801.00362, arXiv.org, revised May 2018.
    10. 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.
    11. Liang-Chih Liu & Chun-Yuan Chiu & Chuan-Ju Wang & Tian-Shyr Dai & Hao-Han Chang, 2022. "Analytical pricing formulae for vulnerable vanilla and barrier options," Review of Quantitative Finance and Accounting, Springer, vol. 58(1), pages 137-170, January.

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