A finite integration method for pricing and hedging path-dependent structured derivatives

Yejin Kim; Wooyeol Jeong; Sungchul Lee; Yejin Kim; Wooyeol Jeong; Sungchul Lee

doi:10.3934/math.20251077

AIMS Mathematics

2025, Volume 10, Issue 10: 24294-24316. doi: 10.3934/math.20251077

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A finite integration method for pricing and hedging path-dependent structured derivatives

1.
EG Asset Pricing Co., Ltd., Seoul 07241, Korea
2.
Department of Mathematics, Yonsei University, Seoul 03722, Korea

Received: 08 July 2025 Revised: 22 September 2025 Accepted: 16 October 2025 Published: 23 October 2025
MSC : 65C20, 91G20

This study introduces the finite integration method (FIM) as a robust numerical approach for pricing equity-linked notes (ELNs). The FIM extends its application beyond vanilla options, effectively addressing the complexities of continuous boundaries and binary payoffs associated with ELNs. We present a comprehensive framework for ELN pricing, including detailed explanations of product structures and a step-by-step description of the FIM methodology. To assess the performance of the FIM, we conduct a comparative analysis against the implicit FDM. Numerical results demonstrate that the FIM outperforms the FDM in terms of reduced pricing errors and more precise hedge parameters (Greeks). We evaluated both one-dimensional barrier options and two-dimensional binary options. Additionally, we proposed an FIM algorithm for pricing a two-dimensional step-down ELN with a knock-in barrier feature. Monte Carlo simulations(MCS) are used as benchmarks to validate the convergence and accuracy of the FIM. The results confirm that the FIM is a robust and practical method for derivative valuation and risk management. Furthermore, the flexibility of the FIM framework allows it to accommodate various complex payoff structures, making it a valuable tool for pricing structured derivatives.
- finite integration method,
- equity-linked notes,
- path-dependent derivatives,
- Greeks,
- numerical methods,
- hedging
Citation: Yejin Kim, Wooyeol Jeong, Sungchul Lee. A finite integration method for pricing and hedging path-dependent structured derivatives[J]. AIMS Mathematics, 2025, 10(10): 24294-24316. doi: 10.3934/math.20251077

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Abstract

This study introduces the finite integration method (FIM) as a robust numerical approach for pricing equity-linked notes (ELNs). The FIM extends its application beyond vanilla options, effectively addressing the complexities of continuous boundaries and binary payoffs associated with ELNs. We present a comprehensive framework for ELN pricing, including detailed explanations of product structures and a step-by-step description of the FIM methodology. To assess the performance of the FIM, we conduct a comparative analysis against the implicit FDM. Numerical results demonstrate that the FIM outperforms the FDM in terms of reduced pricing errors and more precise hedge parameters (Greeks). We evaluated both one-dimensional barrier options and two-dimensional binary options. Additionally, we proposed an FIM algorithm for pricing a two-dimensional step-down ELN with a knock-in barrier feature. Monte Carlo simulations(MCS) are used as benchmarks to validate the convergence and accuracy of the FIM. The results confirm that the FIM is a robust and practical method for derivative valuation and risk management. Furthermore, the flexibility of the FIM framework allows it to accommodate various complex payoff structures, making it a valuable tool for pricing structured derivatives.

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