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Chebyshev Interpolation for Parametric Option Pricing

Author

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  • Maximilian Ga{ss}
  • Kathrin Glau
  • Mirco Mahlstedt
  • Maximilian Mair

Abstract

Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real-time. Simultaneously we observe an increase in model sophistication on the one hand and growing demands on the quality of risk management on the other. To address the resulting computational challenges, it is natural to exploit the recurrent nature of these tasks. We concentrate on Parametric Option Pricing (POP) and show that polynomial interpolation in the parameter space promises to reduce run-times while maintaining accuracy. The attractive properties of Chebyshev interpolation and its tensorized extension enable us to identify criteria for (sub)exponential convergence and explicit error bounds. We show that these results apply to a variety of European (basket) options and affine asset models. Numerical experiments confirm our findings. Exploring the potential of the method further, we empirically investigate the efficiency of the Chebyshev method for multivariate and path-dependent options.

Suggested Citation

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

    1. Mariano Zeron Medina Laris & Ignacio Ruiz, 2018. "Chebyshev Methods for Ultra-efficient Risk Calculations," Papers 1805.00898, arXiv.org.
    2. Yannick Armenti & Stephane Crepey & Samuel Drapeau & Antonis Papapantoleon, 2015. "Multivariate Shortfall Risk Allocation and Systemic Risk," Papers 1507.05351, arXiv.org, revised Mar 2017.
    3. Damien Ackerer & Damir Filipovi'c, 2016. "Linear Credit Risk Models," Papers 1605.07419, arXiv.org, revised Jul 2019.
    4. Ignacio Ruiz & Mariano Zeron, 2018. "Dynamic Initial Margin via Chebyshev Tensors," Papers 1808.08221, arXiv.org, revised Mar 2020.
    5. Philipp Harms, 2019. "Strong convergence rates for Markovian representations of fractional processes," Papers 1902.01471, arXiv.org, revised Aug 2020.
    6. Maximilian Ga{ss} & Kathrin Glau & Maximilian Mair, 2015. "Magic points in finance: Empirical integration for parametric option pricing," Papers 1511.00884, arXiv.org, revised Nov 2016.

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