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Numerical valuation of European options under two-asset infinite-activity exponential L\'evy models

Author

Listed:
  • Massimiliano Moda
  • Karel J. in 't Hout
  • Mich`ele Vanmaele
  • Fred Espen Benth

Abstract

We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential L\'evy models. Our method extends the effective approach developed by Wang, Wan & Forsyth (2007) for the 1-dimensional case to the 2-dimensional setting and is applicable for general L\'evy measures under mild assumptions. A tailored discretization of the non-local integral term is developed, which can be efficiently evaluated by means of the fast Fourier transform. For the temporal discretization, the semi-Lagrangian theta-method is employed in a convenient splitting fashion, where the diffusion term is treated implicitly and the integral term is handled explicitly by a fixed-point iteration. Numerical experiments for put-on-the-average options under Normal Tempered Stable dynamics reveal favourable second-order convergence of our method whenever the exponential L\'evy process has finite-variation.

Suggested Citation

  • Massimiliano Moda & Karel J. in 't Hout & Mich`ele Vanmaele & Fred Espen Benth, 2025. "Numerical valuation of European options under two-asset infinite-activity exponential L\'evy models," Papers 2511.02700, arXiv.org.
    • Handle: RePEc:arx:papers:2511.02700
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    References listed on IDEAS

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    1. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4256-4293.
    2. Marjon Ruijter & Kees Oosterlee, 2012. "Two-dimensional Fourier cosine series expansion method for pricing financial options," CPB Discussion Paper 225, CPB Netherlands Bureau for Economic Policy Analysis.
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