Numerical valuation of European options under two-asset infinite-activity exponential Lévy models
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915900589867008 |
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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 |
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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 |