Numerical valuation of European options under two-asset infinite-activity exponential Lévy models

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Main Authors: Moda, Massimiliano, Hout, Karel J. in 't, Vanmaele, Michèle, Benth, Fred Espen
Format: Preprint
Published: 2025
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author Moda, Massimiliano
Hout, Karel J. in 't
Vanmaele, Michèle
Benth, Fred Espen
author_facet Moda, Massimiliano
Hout, Karel J. in 't
Vanmaele, Michèle
Benth, Fred Espen
contents We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential Lévy 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 Lévy 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 Lévy process has finite-variation.
format Preprint
id arxiv_https___arxiv_org_abs_2511_02700
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Numerical valuation of European options under two-asset infinite-activity exponential Lévy models
Moda, Massimiliano
Hout, Karel J. in 't
Vanmaele, Michèle
Benth, Fred Espen
Numerical Analysis
Computational Finance
We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential Lévy 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 Lévy 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 Lévy process has finite-variation.
title Numerical valuation of European options under two-asset infinite-activity exponential Lévy models
topic Numerical Analysis
Computational Finance
url https://arxiv.org/abs/2511.02700