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

ArXiv ID: 2511.02700 “View on arXiv”

Authors: Massimiliano Moda, Karel J. in ’t Hout, Michèle Vanmaele, Fred Espen Benth

Abstract

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.

Keywords: Lévy processes, Option pricing, Numerical methods, Two-dimensional PDE, Fast Fourier transform, Derivatives

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats

  flowchart TD
    A["Research Goal:<br>Numerical Valuation of European Options<br>under 2-Asset Infinite-Activity Lévy Models"] --> B["Data/Inputs:<br>General Lévy Measures &<br>Underlying Asset Dynamics"]
    B --> C["Key Methodology:<br>Semi-Lagrangian Theta-Method<br>for 2D PDE Time Discretization"]
    C --> D["Computational Process:<br>Tailored Discretization of<br>Non-local Integral Term"]
    D --> E{"Fast Fourier Transform<br>for Efficient Evaluation"}
    E -->|Finite Variation Case| F["Key Findings:<br>Favourable 2nd-Order Convergence"]
    E -->|Infinite Variation Case| F
    F --> G["Outcome:<br>Effective Extension to<br>2D Settings for Put-on-the-Average Options"]