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Counterparty Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method

Author

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  • Patrik Karlsson
  • Shashi Jain
  • Cornelis W. Oosterlee

Abstract

The regulatory credit value adjustment (CVA) for an outstanding over-the-counter (OTC) derivative portfolio is computed based on the portfolio exposure over its lifetime. Usually, the future portfolio exposure is approximated using the Monte Carlo simulation, as the portfolio value can be driven by several market risk-factors. For derivatives, such as Bermudan swaptions, that do not have an analytical approximation for their Mark-to-Market (MtM) value, the standard market practice is to use the regression functions from the least squares Monte Carlo method to approximate their MtM along simulated scenarios. However, such approximations have significant bias and noise, resulting in inaccurate CVA charge. In this paper, we extend the Stochastic Grid Bundling Method (SGBM) for the one-factor Gaussian short rate model, to efficiently and accurately compute Expected Exposure, Potential Future exposure and CVA for Bermudan swaptions. A novel contribution of the paper is that it demonstrates how different measures, for instance spot and terminal measure, can simultaneously be employed in the SGBM framework, to significantly reduce the variance and bias of the solution.

Suggested Citation

  • Patrik Karlsson & Shashi Jain & Cornelis W. Oosterlee, 2016. "Counterparty Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(3), pages 175-196, May.
    • Handle: RePEc:taf:apmtfi:v:23:y:2016:i:3:p:175-196
    DOI: 10.1080/1350486X.2016.1226144
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    Citations

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    Cited by:

    1. Kathrin Glau & Ricardo Pachon & Christian Potz, 2019. "Speed-up credit exposure calculations for pricing and risk management," Papers 1912.01280, arXiv.org.
    2. Ludovic Goudenège & Andrea Molent & Antonino Zanette, 2020. "Computing credit valuation adjustment solving coupled PIDEs in the Bates model," Computational Management Science, Springer, vol. 17(2), pages 163-178, June.
    3. Gijs Mast & Xiaoyu Shen & Fang Fang, 2023. "Fast calculation of Counterparty Credit exposures and associated sensitivities using fourier series expansion," Papers 2311.12575, arXiv.org.
    4. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    5. Shi, Ruoshi & Zhao, Yanlong & Bao, Ying & Peng, Cheng, 2022. "Sensitivity-based Conditional Value at Risk (SCVaR): An efficient measurement of credit exposure for options," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    6. Li, Shuang & Peng, Cheng & Bao, Ying & Zhao, Yanlong, 2020. "Explicit expressions to counterparty credit exposures for Forward and European Option," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    7. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2018. "Computing Credit Valuation Adjustment solving coupled PIDEs in the Bates model," Papers 1809.05328, arXiv.org.
    8. Vikranth Lokeshwar Dhandapani & Shashi Jain, 2024. "Optimizing Neural Networks for Bermudan Option Pricing: Convergence Acceleration, Future Exposure Evaluation and Interpolation in Counterparty Credit Risk," Papers 2402.15936, arXiv.org.

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