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An Analytically Modified Finite Difference Scheme for Pricing Discretely Monitored Options

Author

Listed:
  • Guo Luo

    (Department of Mathematics, Statistics and Insurance, The Hang Seng University of Hong Kong, Hang Shin Link, Siu Lek Yuen, Shatin, N.T., Hong Kong)

  • Min Huang

    (China Merchants Bank, 7088 Shennan Boulevard, Shenzhen 518040, China)

Abstract

Finite difference methods are commonly used in the pricing of discretely monitored exotic options in the Black–Scholes framework, but they tend to converge slowly due to discontinuities contained in terminal conditions. We present an effective analytical modification to existing finite difference methods that greatly enhances their performance on discretely monitored options with non-smooth terminal conditions. We apply this modification to the popular Crank–Nicolson method and obtain highly accurate option pricing results with significantly reduced CPU cost. We also introduce an adaptive mesh refinement technique that further improves the computational speed of the modified finite difference method. The proposed method is especially useful for options with high monitoring frequencies, which are difficult to price using other existing methods.

Suggested Citation

  • Guo Luo & Min Huang, 2025. "An Analytically Modified Finite Difference Scheme for Pricing Discretely Monitored Options," Mathematics, MDPI, vol. 13(2), pages 1-29, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:241-:d:1565533
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    References listed on IDEAS

    as
    1. Gianluca Fusai & I. Abrahams & Carlo Sgarra, 2006. "An exact analytical solution for discrete barrier options," Finance and Stochastics, Springer, vol. 10(1), pages 1-26, January.
    2. Huang, Min & Luo, Guo, 2022. "A simple and efficient numerical method for pricing discretely monitored early-exercise options," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    3. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, October.
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