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A Hybrid Monte Carlo and Finite Difference Method for Option Pricing

Author

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  • Darae Jeong

    (Korea University)

  • Minhyun Yoo

    (Korea University)

  • Changwoo Yoo

    (Korea University)

  • Junseok Kim

    (Korea University)

Abstract

We propose an accurate, efficient, and robust hybrid finite difference method, with a Monte Carlo boundary condition, for solving the Black–Scholes equations. The proposed method uses a far-field boundary value obtained from a Monte Carlo simulation, and can be applied to problems with non-linear payoffs at the boundary location. Numerical tests on power, powered, and two-asset European call option pricing problems are presented. Through these numerical simulations, we show that the proposed boundary treatment yields better accuracy and robustness than the most commonly used linear boundary condition. Furthermore, the proposed hybrid method is general, which means it can be applied to other types of option pricing problems. In particular, the proposed Monte Carlo boundary condition algorithm can be implemented easily in the code of the existing finite difference method, with a small modification.

Suggested Citation

  • Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    • Handle: RePEc:kap:compec:v:53:y:2019:i:1:d:10.1007_s10614-017-9730-4
    DOI: 10.1007/s10614-017-9730-4
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    References listed on IDEAS

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    Cited by:

    1. Sangkwon Kim & Jisang Lyu & Wonjin Lee & Eunchae Park & Hanbyeol Jang & Chaeyoung Lee & Junseok Kim, 2024. "A Practical Monte Carlo Method for Pricing Equity-Linked Securities with Time-Dependent Volatility and Interest Rate," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 2069-2086, May.
    2. Chaeyoung Lee & Soobin Kwak & Youngjin Hwang & Junseok Kim, 2023. "Accurate and Efficient Finite Difference Method for the Black–Scholes Model with No Far-Field Boundary Conditions," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 1207-1224, March.
    3. Kyungwon Kim & Jae Wook Song, 2020. "Detecting Possible Reduction of the Housing Bubble in Korea for Different Residential Types and Regions," Sustainability, MDPI, vol. 12(3), pages 1-31, February.
    4. Lyu, Jisang & Park, Eunchae & Kim, Sangkwon & Lee, Wonjin & Lee, Chaeyoung & Yoon, Sungha & Park, Jintae & Kim, Junseok, 2021. "Optimal non-uniform finite difference grids for the Black–Scholes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 690-704.
    5. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
    6. Seda Gulen & Catalin Popescu & Murat Sari, 2019. "A New Approach for the Black–Scholes Model with Linear and Nonlinear Volatilities," Mathematics, MDPI, vol. 7(8), pages 1-14, August.
    7. Sangkwon Kim & Darae Jeong & Chaeyoung Lee & Junseok Kim, 2020. "Finite Difference Method for the Multi-Asset Black–Scholes Equations," Mathematics, MDPI, vol. 8(3), pages 1-17, March.

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