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All Journal Matematika dan Sains Desimal: Jurnal Matematika MATHunesa: Jurnal Ilmiah Matematika
Rudianto Artiono
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Education Mathematics Social Sciences

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DISCOUNTED FEYNMAN KAC UNTUK MENCARI BENTUK PDP PADA PENENTUAN HARGA OPSI SAHAM KARYAWAN SETELAH VESTING PERIOD Rudianto Artiono,
Matematika dan Sains Vol 18, No 1 (2011)
Publisher : Matematika dan Sains

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Abstract

One of the compensation form which can given by the business to employee was Opsi Saham Karyawan (OSK). It gave right to employee to buy a part of the business share at a period in future with the fixed value. In giving OSK, there are fitures to accommodate the needs of business and employee attitudes. The fitures used in determination of OSK with the Verr model are vesting period, exit rate, reload, and reset. Discounted Feynman Kac can be used to find the partial differential equation to determine the value of OSK after pass the vesting period.
PEMODELAN HARGA SAHAM DENGAN PEMBAGIAN DIVIDEN MENGGUNAKAN GEOMETRIC BROWNIAN MOTION DAN SIMULASI MONTE CARLO Firdaus, Anjali Wardha; Rudianto Artiono
MATHunesa: Jurnal Ilmiah Matematika Vol. 13 No. 2 (2025)
Publisher : Universitas Negeri Surabaya

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Abstract

Pada saat ini investasi merupakan salah satu kegiatan ekonomi yang semakin populer di masyarakat. Salah satu jenis investasi adalah investasi berupa saham. Beberapa perusahaan yang menawarkan investasi saham bagi para investor juga membagikan laba yang diperoleh perusahaan dengan membagikannya dalam bentuk dividen kepada para investor saham. Model Geometric Brownian Motion dengan kombinasi simulasi Monte Carlo dapat memperoleh tingkat akurasi kurang dari 10% di beberapa kasus dalam memprediksi harga saham. Namun, penelitian terkait prediksi harga saham yang mengasumsikan pembagian dividen masih terbatas, padahal dividen merupakan salah satu faktor yang mempengaruhi minat investor dalam berinvestasi saham. Oleh karena itu, penelitian ini bertujuan untuk memodelkan harga saham dengan pembagian dividen menggunakan Geometric Brownian Motion dan Simulasi Monte Carlo. Dari hasil simulasi model, didapatkan keakuratan nilai MAPE sebesar 1,59% ketika simulasi dilakukan dengan 100000 iterasi, yang artinya dapat dikatakan tingkat keakuratan model tersebut dalam memprediksi harga saham adalah sangat akurat.
ANALISI DINAMIK MODEL KOINFEKSI PENYEBARAN PENYAKIT FLU BABI (H1N1) DAN FLU BURUNG (H5N1) Evi Khoirotun Nisa, Evi Khoirotun Nisa; Rudianto Artiono
MATHunesa: Jurnal Ilmiah Matematika Vol. 13 No. 2 (2025)
Publisher : Universitas Negeri Surabaya

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A semidiscretization scheme for european option pricing based on the black scholes model Nur Annisa Mulia; Rudianto Artiono
Desimal: Jurnal Matematika Vol. 8 No. 3 (2025): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v8i3.202529273

Abstract

The development of derivative instruments in modern financial markets has created a growing need for option pricing methods that are both accurate and easy to implement. This study aims to calculate the price of European call options using the Black-Scholes model through a semidiscretization numerical approach. The method used involves time transformation, discretization of space variables, and explicit Euler scheme iteration to obtain numerical solutions. This method is applied to real stock price data, and the numerical results are compared with the Black-Scholes analytical solution at various grid numbers. The results show that accuracy increases with the number of grids, and the relative error is very small when M is large enough, so that this method is capable of producing a numerical approximation that is consistent with the analytical solution. These findings also confirm the trade-off between efficiency and accuracy,but still show that semidiscretization can be a practical, fast, and flexible alternative when analytical solutions are difficult to use or when parameter changes need to be evaluated dynamically. This research contributes by showing that a simple numerical approach can still work effectively in real market conditions, making it a practical and efficient alternative for analysts who need fast and flexible calculations without the complexity of advanced numerical methods.
Co-Authors Evi Khoirotun Nisa, Evi Khoirotun Nisa Firdaus, Anjali Wardha Nur Annisa Mulia