Numerical methods for solving PIDEs arising in swing option pricing under a two-factor mean-reverting model with jumps

ArXiv ID: 2511.01587 “View on arXiv”

Authors: Mustapha Regragui, Karel J. in ’t Hout, Michèle Vanmaele, Fred Espen Benth

Abstract

This paper concerns the numerical valuation of swing options with discrete action times under a linear two-factor mean-reverting model with jumps. The resulting sequence of two-dimensional partial integro-differential equations (PIDEs) are convection-dominated and possess a nonlocal integral term due to the presence of jumps. Further, the initial function is nonsmooth. We propose various second-order numerical methods that can adequately handle these challenging features. The stability and convergence of these numerical methods are analysed theoretically. By ample numerical experiments, we confirm their second-order convergence behaviour.

Keywords: swing options, partial integro-differential equations, finite difference methods, mean-reverting model, jump diffusion

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced PIDE theory with detailed stability and convergence proofs, yet it lacks real-world backtesting, focusing instead on synthetic numerical experiments for convergence validation.

  flowchart TD
    A["Research Goal:<br>Numerical Valuation of Swing Options<br>under a 2-factor Mean-Reverting Jump Model"] --> B["Modeling Step:<br>Derivation of 2D Linear PIDEs<br>(Convection-dominated + Jumps)"]
    B --> C["Discretization Step:<br>Second-order Finite Difference Schemes<br>(ADI / Operator Splitting)"]
    C --> D["Computational Process:<br>Stability & Convergence Analysis<br>via von Neumann / Matrix Stability"]
    C --> E["Validation Step:<br>Numerical Experiments on<br>Discrete Action Times & Nonsmooth Data"]
    D --> F["Key Findings/Outcomes:<br>Stable 2nd-order convergence achieved<br>Robust handling of jump terms & convection"]
    E --> F