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Finite Element Solution of the Two-Dimensional Bates Model for Option Pricing Under Stochastic Volatility and Jumps

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  • Neda Bagheri Renani
  • Daniel Sevcovic

Abstract

We propose a fourth--order compact finite--difference (HOC--FD) scheme for the transformed Bates partial integro--differential equation (PIDE). The method employs an implicit--explicit (IMEX) Crank--Nicolson framework for local terms and Simpson quadrature for the jump integral. Benchmarks against second--order finite differences (FD) and quadratic finite elements (FEM, p=2) confirm near--fourth--order spatial accuracy for HOC--FD, near--second--order for FEM, and second--order temporal convergence for all time integrators. Efficiency tests show that HOC--FD achieves similar accuracy at up to two orders of magnitude lower runtime than FEM, establishing it as a practical baseline for option pricing under stochastic volatility jump--diffusion models.

Suggested Citation

  • Neda Bagheri Renani & Daniel Sevcovic, 2026. "Finite Element Solution of the Two-Dimensional Bates Model for Option Pricing Under Stochastic Volatility and Jumps," Papers 2602.19092, arXiv.org.
    • Handle: RePEc:arx:papers:2602.19092
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    File URL: http://arxiv.org/pdf/2602.19092
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