ANALYSIS OF SOLVING THE BLACK-SCHOLES EQUATION USING THE FINITE DIFFERENCE METHOD WITH A NON-UNIFORM GRID

Authors

  • Manisya Bulandari Department of Mathematics and Data Science, Universitas Andalas
  • Mahdhivan Syafwan Department of Mathematics and Data Science, Universitas Andalas
  • Yudiantri Asdi Department of Mathematics and Data Science, Universitas Andalas

DOI:

https://doi.org/10.25077/jmua.14.4.451-462.2025

Keywords:

Persamaan Black-Scholes, opsi call, metode beda hingga, grid tidak seragam

Abstract

Artikel ini mengimplementasikan metode beda hingga dengan skema eksplisit berbasis grid tidak seragam pada persamaan Black–Scholes untuk menghitung harga opsi call Eropa. Skema diturunkan menggunakan deret Taylor sehingga diperoleh sistem persamaan beda yang kemudian ditransformasikan ke dalam bentuk matriks dan diselesaikan secara rekursif melalui pemrograman Matlab. Berdasarkan simulasi numerik untuk nilai-nilai parameter tertentu, hasil yang diperoleh menunjukkan bahwa skema beda hingga dengan grid tidak seragam menghasilkan solusi yang lebih akurat dibandingkan grid seragam. Galat relatif lebih besar untuk harga saham yang berada di sekitar harga pelaksanaan, tetapi dapat dikurangi secara signifikan melalui penggunaan grid tidak seragam. Selain itu, pendekatan grid tidak seragam memberikan efisiensi komputasi yang lebih baik dibandingkan skema seragam.

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Author Biography

Mahdhivan Syafwan, Department of Mathematics and Data Science, Universitas Andalas

Scopus ID = 57190938540

References

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Published

31-10-2025

How to Cite

Bulandari, M., Syafwan, M., & Asdi, Y. (2025). ANALYSIS OF SOLVING THE BLACK-SCHOLES EQUATION USING THE FINITE DIFFERENCE METHOD WITH A NON-UNIFORM GRID. Jurnal Matematika UNAND, 14(4), 451–462. https://doi.org/10.25077/jmua.14.4.451-462.2025

Issue

Vol. 14 No. 4 (2025)

Section

Articles

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