An Analytically Modified Finite Difference Scheme for Pricing Discretely Monitored Options

Guo Luo () and Min Huang
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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

Mathematics, 2025, vol. 13, issue 2, 1-29

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.

Keywords: discrete option pricing; finite difference method; analytical modification; autocallable structured product; barrier option; snowball option (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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