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Computing credit valuation adjustment solving coupled PIDEs in the Bates model

Author

Listed:
  • Ludovic Goudenège

    (Féderation de Mathématiques de CentraleSupélec - CNRS FR3487)

  • Andrea Molent

    (Università degli Studi di Udine)

  • Antonino Zanette

    (Università degli Studi di Udine)

Abstract

Credit Value Adjustment is the charge applied by financial institutions to the counter-party to cover the risk of losses on a counterpart default event. In this paper we estimate such a premium under the Bates stochastic model (Bates in The Review of Financial Studies 9(1): 69–107, 1996), which considers an underlying affected by both stochastic volatility and random jumps. We propose an efficient method which improves the Finite-Difference Monte Carlo (FDMC) approach introduced by de Graaf et al. (Journal of Computational Finance 21, 2017) In particular, the method we propose consists in replacing the Monte Carlo step of the FDMC approach with a finite difference step and the whole method relies on the efficient solution of two coupled partial integro-differential equations which is done by employing the Hybrid Tree-Finite Difference method developed by Briani et al. ( arXiv:1603.07225 2016;IMA Journal of Management Mathematics 28(4): 467–500, 2017;The Journal of Computational Finance 21(3): 1–45, 2017). Moreover, the direct application of the hybrid techniques in the original FDMC approach is also considered for comparison purposes. Several numerical tests prove the effectiveness and the reliability of the proposed approach when both European and American options are considered. Subject classification numbers as needed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comgts:v:17:y:2020:i:2:d:10.1007_s10287-020-00365-6
    DOI: 10.1007/s10287-020-00365-6
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    References listed on IDEAS

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    1. Maya Briani & Lucia Caramellino & Antonino Zanette, 2017. "A hybrid approach for the implementation of the Heston model," Post-Print hal-00916440, HAL.
    2. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    3. Ludovic Goudenege & Andrea Molent & Antonino Zanette, 2019. "Pricing and hedging GMWB in the Heston and in the Black–Scholes with stochastic interest rate models," Computational Management Science, Springer, vol. 16(1), pages 217-248, February.
    4. Rong, Situ, 1997. "On solutions of backward stochastic differential equations with jumps and applications," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 209-236, March.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. Mark Joshi & Oh Kang Kwon, 2016. "Least Squares Monte Carlo Credit Value Adjustment With Small And Unidirectional Bias," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-16, December.
    7. Patrice Gaillardetz & Joe Youssef Lakhmiri, 2011. "A New Premium Principle for Equity‐Indexed Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(1), pages 245-265, March.
    8. Jain, Shashi & Oosterlee, Cornelis W., 2015. "The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 412-431.
    9. Maya Briani & Lucia Caramellino & Antonino Zanette, 2013. "A hybrid approach for the implementation of the Heston model," Papers 1307.7178, arXiv.org, revised Sep 2017.
    10. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    11. 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.
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    Cited by:

    1. Ludovic Goudenege & Andrea Molent & Antonino Zanette, 2022. "Computing XVA for American basket derivatives by Machine Learning techniques," Papers 2209.06485, arXiv.org.

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