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

2025-11-03

AI Summary

This work addresses the pricing of discrete-time swing options under a two-factor mean-reverting model with jumps, leading to a sequence of two-dimensional convection-dominated partial integro-differential equations (PIDEs) featuring nonlocal jump integral terms and nonsmooth initial data. We propose a second-order unconditionally stable finite difference scheme that combines efficient convolution-based approximation of the nonlocal integral term with an iterative time-stepping strategy, enabling explicit treatment of both the jump operator and initial singularities. Theoretical analysis establishes unconditional stability and second-order convergence in space and time. Numerical experiments confirm high accuracy and robustness across diverse parameter regimes. The method significantly enhances computational efficiency and reliability for pricing complex energy derivatives—particularly multi-exercise swing options—and provides a scalable, high-accuracy framework for solving high-dimensional financial PIDEs incorporating jump dynamics.

Technology Category

Search and Optimization: Non-convex OptimizationReasoning under Uncertainty: Stochastic OptimizationConstraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchangesGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSecurity and Privacy: Large-scale security measurements

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.

Problem

• Solving PIDEs for swing option pricing with jumps
• Handling convection-dominated equations with nonlocal integral terms
• Developing second-order methods for nonsmooth initial conditions

Innovation

• Second-order numerical methods for PIDEs
• Handles convection-dominated equations with jumps
• Analyzes stability and convergence theoretically