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Efficient Computation Of Exposure Profiles For Counterparty Credit Risk

Author

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  • CORNELIS S. L. DE GRAAF

    (Computational Science, University of Amsterdam, Science Park 904, Amsterdam, 1098 XH, The Netherlands)

  • QIAN FENG

    (CWI – The Center for Mathematics and Computer Science, Science Park 123, Amsterdam, 1098 XG, The Netherlands)

  • DRONA KANDHAI

    (Quantitative Analytics, ING Bank, Bijlmerdreef 98, Amsterdam, 1102 CT, The Netherlands;
    Computational Science, University of Amsterdam, Science Park 904, Amsterdam, 1098 XH, The Netherlands)

  • CORNELIS W. OOSTERLEE

    (CWI – The Center for Mathematics and Computer Science, Science Park 123, Amsterdam, 1098 XG, The Netherlands;
    Delft University of Technology, DIAM – Delft Institute of Applied Mathematics, Mekelweg 4, Delft, 2628 CD, The Netherlands)

Abstract

Three computational techniques for approximation of counterparty exposure for financial derivatives are presented. The exposure can be used to quantify so-called Credit Valuation Adjustment (CVA) and Potential Future Exposure (PFE), which are of utmost importance for modern risk management in the financial industry, especially since the recent credit crisis. The three techniques all involve a Monte Carlo path discretization and simulation of the underlying entities. Along the generated paths, the corresponding values and distributions are computed during the entire lifetime of the option. Option values are computed by either the finite difference method for the corresponding partial differential equations, or the simulation-based Stochastic Grid Bundling Method (SGBM), or by the COS method, based on Fourier-cosine expansions. In this research, numerical results are presented for early-exercise options. The underlying asset dynamics are given by either the Black–Scholes or the Heston stochastic volatility model.

Suggested Citation

  • Cornelis S. L. De Graaf & Qian Feng & Drona Kandhai & Cornelis W. Oosterlee, 2014. "Efficient Computation Of Exposure Profiles For Counterparty Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-23.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:04:n:s0219024914500241
    DOI: 10.1142/S0219024914500241
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    References listed on IDEAS

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    1. Tinne Haentjens & Karel in 't Hout, 2013. "ADI schemes for pricing American options under the Heston model," Papers 1309.0110, arXiv.org.
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    Citations

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    Cited by:

    1. Patrik Karlsson & Shashi Jain & Cornelis W. Oosterlee, 2016. "Fast and accurate exercise policies for Bermudan swaptions in the LIBOR market model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-22, March.
    2. Andersson, Kristoffer & Oosterlee, Cornelis W., 2021. "A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    3. Salvador, Beatriz & Oosterlee, Cornelis W., 2021. "Corrigendum to ``Total value adjustment for a stochastic volatility model. A comparison with the Black–Scholes model''," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    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. Ludovic Goudenege & Andrea Molent & Antonino Zanette, 2022. "Computing XVA for American basket derivatives by Machine Learning techniques," Papers 2209.06485, arXiv.org.
    6. Salvador, Beatriz & Oosterlee, Cornelis W., 2021. "Total value adjustment for a stochastic volatility model. A comparison with the Black–Scholes model," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    7. Purba Banerjee & Vasudeva Murthy & Shashi Jain, 2024. "Method of Lines for Valuation and Sensitivities of Bermudan Options," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 245-270, January.
    8. Anastasia Borovykh & Andrea Pascucci & Cornelis W. Oosterlee, 2019. "Efficient Computation of Various Valuation Adjustments Under Local L\'evy Models," Papers 1905.01706, arXiv.org.
    9. Cornelis S. L. de Graaf & Drona Kandhai & Christoph Reisinger, 2016. "Efficient exposure computation by risk factor decomposition," Papers 1608.01197, arXiv.org, revised Feb 2018.
    10. T. van der Zwaard & L. A. Grzelak & C. W. Oosterlee, 2024. "On the Hull-White model with volatility smile for Valuation Adjustments," Papers 2403.14841, arXiv.org.
    11. Q. Feng & C. W. Oosterlee, 2014. "Monte Carlo Calculation of Exposure Profiles and Greeks for Bermudan and Barrier Options under the Heston Hull-White Model," Papers 1412.3623, arXiv.org.
    12. 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.
    13. Purba Banerjee & Vasudeva Murthy & Shashi Jain, 2021. "Method of lines for valuation and sensitivities of Bermudan options," Papers 2112.01287, arXiv.org.

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