A Semi-Analytical Approach to Solving the Black-Scholes Equation via Reproducing Kernel Hilbert Spaces (RKHS)

Application to Synthetic and Real Financial Data (AAPL)

Authors

  • Erisbey Marin Departamento de Matem´aticas, Universidad Tecnol´ogica de Pereira, Pereira 660003, Colombia
  • Edgar Alirio Valencia Departamento de Matem´aticas, Universidad Tecnol´ogica de Pereira, Pereira 660003, Colombia
  • Carlos Alberto Ramirez Departamento de Matem´aticas, Universidad Tecnol´ogica de Pereira, Pereira 660003, Colombia

DOI:

https://doi.org/10.19139/soic-2310-5070-2874

Keywords:

Black-Scholes equation, Stochastic differential equations (SDEs), Reproducing Kernel Hilbert Spaces (RKHS), Gaussian kernels, Option pricing.

Abstract

This paper presents a semi–analytical method for solving the Black–Scholes equation by embedding its deterministic and stochastic components into a Reproducing Kernel Hilbert Space (RKHS). The deterministic term is approximated via regularized kernel regression, while the stochastic term is modeled using an autoregressive representation in RKHS. The method is validated on both synthetic geometric Brownian motion trajectories and real adjusted closing prices of Apple Inc. (AAPL), comparing the RKHS approach against the Euler–Maruyama scheme. Results show that the proposed method achieves lower RMSE with fewer anchor points, demonstrating its efficiency and robustness for data–driven financial modeling under uncertainty.

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Published

2025-09-18

Issue

Vol. 14 No. 5 (2025)

Section

Research Articles

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How to Cite

A Semi-Analytical Approach to Solving the Black-Scholes Equation via Reproducing Kernel Hilbert Spaces (RKHS): Application to Synthetic and Real Financial Data (AAPL). (2025). Statistics, Optimization & Information Computing, 14(5), 2903-2913. https://doi.org/10.19139/soic-2310-5070-2874

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