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Chebyshev Greeks: Smoothing Gamma without Bias

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  • Andrea Maran
  • Andrea Pallavicini
  • Stefano Scoleri

Abstract

The computation of Greeks is a fundamental task for risk managing of financial instruments. The standard approach to their numerical evaluation is via finite differences. Most exotic derivatives are priced via Monte Carlo simulation: in these cases, it is hard to find a fast and accurate approximation of Greeks, mainly because of the need of a tradeoff between bias and variance. Recent improvements in Greeks computation, such as Adjoint Algorithmic Differentiation, are unfortunately uneffective on second order Greeks (such as Gamma), which are plagued by the most significant instabilities, so that a viable alternative to standard finite differences is still lacking. We apply Chebyshev interpolation techniques to the computation of spot Greeks, showing how to improve the stability of finite difference Greeks of arbitrary order, in a simple and general way. The increased performance of the proposed technique is analyzed for a number of real payoffs commonly traded by financial institutions.

Suggested Citation

  • Andrea Maran & Andrea Pallavicini & Stefano Scoleri, 2021. "Chebyshev Greeks: Smoothing Gamma without Bias," Papers 2106.12431, arXiv.org.
    • Handle: RePEc:arx:papers:2106.12431
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    References listed on IDEAS

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    1. 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.
    2. Mariano Zeron Medina Laris & Ignacio Ruiz, 2018. "Chebyshev Methods for Ultra-efficient Risk Calculations," Papers 1805.00898, arXiv.org.
    3. Mariano Zeron & Ignacio Ruiz, 2020. "Tensoring volatility calibration," Papers 2012.07440, arXiv.org, revised Dec 2020.
    4. Marco Bianchetti & Sergei Kucherenko & Stefano Scoleri, 2015. "Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis," Papers 1504.02896, arXiv.org.
    5. Maximilian Gaß & Kathrin Glau & Mirco Mahlstedt & Maximilian Mair, 2018. "Chebyshev interpolation for parametric option pricing," Finance and Stochastics, Springer, vol. 22(3), pages 701-731, July.
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    Cited by:

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    2. Glau, Kathrin & Wunderlich, Linus, 2022. "The deep parametric PDE method and applications to option pricing," Applied Mathematics and Computation, Elsevier, vol. 432(C).

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