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Chebyshev Methods for Ultra-efficient Risk Calculations

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  • Mariano Zeron Medina Laris
  • Ignacio Ruiz

Abstract

Financial institutions now face the important challenge of having to do multiple portfolio revaluations for their risk computation. The list is almost endless: from XVAs to FRTB, stress testing programs, etc. These computations require from several hundred up to a few million revaluations. The cost of implementing these calculations via a "brute-force" full revaluation is enormous. There is now a strong demand in the industry for algorithmic solutions to the challenge. In this paper we show a solution based on Chebyshev interpolation techniques. It is based on the demonstrated fact that those interpolants show exponential convergence for the vast majority of pricing functions that an institution has. In this paper we elaborate on the theory behind it and extend those techniques to any dimensionality. We then approach the problem from a practical standpoint, illustrating how it can be applied to many of the challenges the industry is currently facing. We show that the computational effort of many current risk calculations can be decreased orders of magnitude with the proposed techniques, without compromising accuracy. Illustrative examples include XVAs and IMM on exotics, XVA sensitivities, Initial Margin Simulations, IMA-FRTB and AAD.

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  • Mariano Zeron Medina Laris & Ignacio Ruiz, 2018. "Chebyshev Methods for Ultra-efficient Risk Calculations," Papers 1805.00898, arXiv.org.
    • Handle: RePEc:arx:papers:1805.00898
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    References listed on IDEAS

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    1. Maximilian Ga{ss} & Kathrin Glau & Mirco Mahlstedt & Maximilian Mair, 2015. "Chebyshev Interpolation for Parametric Option Pricing," Papers 1505.04648, arXiv.org, revised Jul 2016.
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    Cited by:

    1. Andrea Maran & Andrea Pallavicini & Stefano Scoleri, 2021. "Chebyshev Greeks: Smoothing Gamma without Bias," Papers 2106.12431, arXiv.org.
    2. Mariano Zeron & Ignacio Ruiz, 2020. "Dynamic sensitivities and Initial Margin via Chebyshev Tensors," Papers 2011.04544, arXiv.org.
    3. Grzelak, Lech A., 2022. "Sparse grid method for highly efficient computation of exposures for xVA," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    4. Mariano Zeron-Medina Laris & Ignacio Ruiz, 2019. "Denting the FRTB IMA computational challenge via Orthogonal Chebyshev Sliding Technique," Papers 1911.10948, arXiv.org, revised Dec 2020.
    5. Lech A. Grzelak, 2021. "Sparse Grid Method for Highly Efficient Computation of Exposures for xVA," Papers 2104.14319, arXiv.org, revised May 2022.
    6. Darrold Cordes & Shahram Latifi & Gregory M. Morrison, 2022. "Systematic literature review of the performance characteristics of Chebyshev polynomials in machine learning applications for economic forecasting in low-income communities in sub-Saharan Africa," SN Business & Economics, Springer, vol. 2(12), pages 1-33, December.

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