Numerical valuation of European options under two-asset infinite-activity exponential L\'evy models
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.
Keywords
Cite
@article{arxiv.2511.02700,
title = {Numerical valuation of European options under two-asset infinite-activity exponential L\'evy models},
author = {Massimiliano Moda and Karel J. in 't Hout and Michèle Vanmaele and Fred Espen Benth},
journal= {arXiv preprint arXiv:2511.02700},
year = {2026}
}