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AAD and least-square Monte Carlo: Fast Bermudan-style options and XVA Greeks

Author

Listed:
  • Capriotti, Luca

    (Quantitative Strategies, Global Markets, Credit Suisse Group, One Cabot Square and Department of Mathematics, University College London)

  • Jiang, Yupeng

    (Department of Mathematics, University College London)

  • Macrina, Andrea

    (Department of Mathematics, University College London and Department of Actuarial Science, University of Cape Town)

Abstract

We show how Adjoint Algorithmic Differentiation (AAD) can be used to calculate price sensitivities in regression-based Monte Carlo methods reliably and orders of magnitude faster than with standard finite-difference approaches. We present the AAD version of the celebrated least-square algorithms of Tsitsiklis and Van Roy (2001) and Longstaff and Schwartz (2001) . By discussing in detail examples of practical relevance, we demonstrate how accounting for the contributions associated with the regression functions is crucial to obtain accurate estimates of the Greeks, especially in XVA applications.

Suggested Citation

  • Capriotti, Luca & Jiang, Yupeng & Macrina, Andrea, 2017. "AAD and least-square Monte Carlo: Fast Bermudan-style options and XVA Greeks," Algorithmic Finance, IOS Press, vol. 6(1-2), pages 35-49.
    • Handle: RePEc:ris:iosalg:0057
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    Citations

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    Cited by:

    1. Griselda Deelstra & Lech A. Grzelak & Felix L. Wolf, 2022. "Accelerated Computations of Sensitivities for xVA," Papers 2211.17026, arXiv.org, revised Jan 2024.
    2. Mike Ludkovski & Yuri Saporito, 2020. "KrigHedge: Gaussian Process Surrogates for Delta Hedging," Papers 2010.08407, arXiv.org, revised Jan 2022.
    3. Kathrin Glau & Daniel Kressner & Francesco Statti, 2019. "Low-rank tensor approximation for Chebyshev interpolation in parametric option pricing," Papers 1902.04367, arXiv.org.

    More about this item

    Keywords

    Adjoint algorithmic differentiation (AAD); Monte Carlo methods; Bermudan-style options; valuation adjustments (XVA);
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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