ANALYSIS OF SOLVING THE BLACK-SCHOLES EQUATION USING THE FINITE DIFFERENCE METHOD WITH A NON-UNIFORM GRID
DOI:
https://doi.org/10.25077/jmua.14.4.451-462.2025Keywords:
Persamaan Black-Scholes, opsi call, metode beda hingga, grid tidak seragamAbstract
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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