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A note on the numerical approximation of Greeks for American-style options

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  • Hout, Karel J. in ’t

Abstract

In this note, we consider the approximation of the Greeks Delta and Gamma of American-style options through the numerical solution of time-dependent partial differential complementarity problems (PDCPs). This approach is very attractive as it can yield accurate approximations to these Greeks at essentially no additional computational cost during the numerical solution of the PDCP for the pertinent option value function. For the temporal discretization, the Crank–Nicolson method is arguably the most popular method in computational finance. It is well-known, however, that this method can have an undesirable convergence behaviour in the approximation of the Greeks Delta and Gamma for American-style options, even when backward Euler damping (Rannacher smoothing) is employed.

Suggested Citation

  • Hout, Karel J. in ’t, 2025. "A note on the numerical approximation of Greeks for American-style options," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 501-516.
    • Handle: RePEc:eee:matcom:v:230:y:2025:i:c:p:501-516
    DOI: 10.1016/j.matcom.2024.10.038
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    References listed on IDEAS

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    1. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    2. Sam Howison & Christoph Reisinger & Jan Hendrik Witte, 2010. "The Effect of Non-Smooth Payoffs on the Penalty Approximation of American Options," Papers 1008.0836, arXiv.org, revised May 2013.
    3. Karel in 't Hout & Pieter Lamotte, 2022. "Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model," Papers 2207.10060, arXiv.org, revised May 2023.
    4. Khaliq, A.Q.M. & Voss, D.A. & Kazmi, S.H.K., 2006. "A linearly implicit predictor-corrector scheme for pricing American options using a penalty method approach," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 489-502, February.
    5. Khaliq, A.Q.M. & Voss, D.A. & Yousuf, M., 2007. "Pricing exotic options with L-stable Pade schemes," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3438-3461, November.
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