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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Juring (Journal for Research in Mathematics Learning) BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Abdimas PHB : Jurnal Pengabdian Masyarakat Progresif Humanis Brainstorming M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika JCER (Journal of Chemistry Education Research) Jurnal Magister Pendidikan Matematika (JUMADIKA) SEPREN: Journal of Mathematics Education and Applied Jurnal Penelitian Pendidikan Matematika dan Sains Jurnal Impresi Indonesia MATHunesa: Jurnal Ilmiah Matematika JANITA Jurnal Karya Abdi Masyarakat
RUDIANTO ARTIONO, RUDIANTO
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Analisis Matematika dan Simulasi Numerik Model Penyebaran Penyakit Leptospirosis pada Manusia dengan Kesadaran Pola Hidup Bersih dan Sehat Yaqin, Mohammad Iqbal Ainul; Agustin, Agil Dwi; Artiono, Rudianto
Sepren Vol 7 No 01 (2025): Edisi November 2025
Publisher : Prodi Pendidikan Matematika FKIP Universitas HKBP Nommensen

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36655/sepren.v7i01.2006

Abstract

Leptospirosis merupakan penyakit zoonosis yang ditularkan melalui air dan hewan vektor, terutama tikus. Penelitian ini membahas model matematika penyebaran leptospirosis pada manusia dengan mempertimbangkan kesadaran pola hidup bersih dan sehat serta interaksi dengan hewan vektor tikus. Model disusun dalam bentuk sistem persamaan diferensial dan dianalisis menggunakan metode Next Generation Matrix (NGM) untuk menentukan bilangan reproduksi dasar (R0). Analisis kestabilan dilakukan melalui nilai eigen dari matriks Jacobian pada titik kesetimbangan bebas penyakit. Hasil penelitian menunjukkan dua titik kesetimbangan, yaitu kesetimbangan bebas penyakit dan kesetimbangan endemik. Simulasi numerik memperlihatkan bahwa peningkatan laju kematian alami tikus (eta_r) dan penerapan pola hidup bersih dan sehat dapat menurunkan penyebaran penyakit leptospirosis pada manusia.
MODEL MATEMATIKA PENILAIAN OPSI SAHAM KARYAWAN MENGGUNAKAN METODE POHON BINOMIAL Fitroh, Dewi Laily; Artiono, Rudianto
MATHunesa: Jurnal Ilmiah Matematika Vol. 11 No. 3 (2023)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v11n3.p360-367

Abstract

Opsi Saham Karyawan, yang selanjutnya disebut OSK, merupakan salah satu sistem kompensasi berbentuk pemberian hak oleh perusahaan terhadap karyawan untuk membeli (call) sejumlah saham perusahaan pada harga yang telah ditentukan sebelumnya (strike price) dalam suatu periode waktu. OSK sendiri termasuk dalam kategori biaya/beban dalam laporan laba-rugi perusahaan. Sebelum OSK dilimpahkan, perusahaan perlu mengetahui harga atau nilai dari OSK tersebut untuk dianggarkan pada laporan tersebut. Metode penilaian yang dapat diterapkan ke opsi saham karyawan dan dibahas pada Skripsi ini adalah metode pohon binomial/binomial tree. Metode pohon binomial pertama kali dikembangkan oleh Cox, Ross, dan Ruberstain pada tahun 1979 dengan mengasumsikan bahwa harga saham di masa mendatang akan bergerak naik atau turun. Hasil simulasi penilaian OSK dari studi kasus salah satu perusahaan yang tercatat pada Bursa Efek Indonesia selama Januari 2023-April 2023 menggunakan Google Sheets adalah 795.8738647. Lalu, untuk hasil simulasi menggunakan Google Colaboratory (python programming) dengan data yang sama adalah 797.496987. Berdasarkan analisis pengaruh variabel terhadap nilai OSK yang telah dilakukan, disimpulkan bahwa nilai variabel durasi OSK dan banyaknya periode berbanding lurus dengan nilai OSK, sedangkan nilai variabel strike price dan exit rate berbanding terbalik dengan nilai OSK. Kata Kunci: Model Matematika, Penilaian Opsi Saham Karyawan, Opsi Bergaya Eropa, Metode Pohon Binomial Cox-Ross-Ruberstain (CRR).
PEMODELAN MATEMATIKA OPSI SAHAM KARYAWAN YANG MEMPERTIMBANGKAN EFEK DILUSI Taufiqi, Nuril Hidayah; Artiono, Rudianto
MATHunesa: Jurnal Ilmiah Matematika Vol. 11 No. 3 (2023)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v11n3.p414-421

Abstract

Implementation of Problem Based Learning Model to Improve the Ability to Solve SPLDV in Grade 9 Students Akhiroh, Mazro’atul; Artiono, Rudianto; Rachman, Kamadiyati
Jurnal Impresi Indonesia Vol. 3 No. 10 (2024): Jurnal Impresi Indonesia
Publisher : Riviera Publishing

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58344/jii.v3i10.5585

Abstract

This research focuses on the challenges in learning mathematics, especially in understanding and solving the system of linear equations of two variables, which is often an obstacle for students. This study aims to improve students' ability to solve SPLDV as well as increase students' motivation and engagement in learning. This study analyzed the effectiveness of Problem Based Learning (PBL) model in improving the ability to solve the System of Linear Equations of Two Variables (SPLDV) in class VIII students of SMPN 54 Surabaya. This study involved 34 students consisting of 18 male students and 16 female students using a Classroom Action Research (PTK) approach carried out in two cycles, each of which consisted of planning, action implementation, observation, and reflection stages. The instruments used were learning outcome tests, observation sheets, and student questionnaires. The results showed a significant increase in students' SPLDV problem solving ability, with the average score of students increasing from 65 in the pretest to 75 in the first cycle post-test, and reached 85 in the second cycle post-test. The proportion of students who met the Minimum Completion Criteria (KKM) increased from 50% in the first cycle to 85% in the second cycle. Further analysis showed that female students outperformed male students, with an average score of 87 and 82. Student engagement also increased, reaching 90% in the second cycle. This study concludes that the PBL model effectively improved SPLDV problem solving skills in grade 9 students and recommends its wider application in mathematics education.
Penerapan Problem Based Learning untuk Meningkatkan Hasil Belajar Peserta Didik SMP sesuai Kurikulum Merdeka Lestari, Endri Puji; Artiono, Rudianto; Postekoningsih, Dwi Rahaju
Juring (Journal for Research in Mathematics Learning) Vol 7, No 1 (2024)
Publisher : Universitas Islam Negeri Sultan Syarif Kasim Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24014/juring.v7i1.25258

Abstract

This research started with low pre-test results for class VII F of SMP Negeri 52 Surabaya when solving problems in statistics material. The pre test is given during the pre cycle, before giving action in the form of applying the problem based learning (PBL) model in learning. Of the 29 students with the Learning Objectives Achievement Criteria (KKTP) it showed that 44.83% of students had not achieved completeness. Classroom Action Research (CAR) was conducted to find out the increase in student learning outcomes with the problem-based learning model according to the independent curriculum. The research subjects were class VII F students, totaling 29 students. The time of the research was carried out in 2 cycles, namely from May 15 2023 to July 28 2023. The research instruments were learning achievement tests, observations and unstructured interviews. Based on the results of the study, namely 1) pre-cycle, the learning outcomes that achieved a completeness score of 16 students were 55.17% and the average learning outcomes were 54.86 in the low PAP category (2) cycle 1, learning outcomes that achieved a completeness score of 20 students by 68.96% and the average value of learning outcomes is 78.56 with the moderate LAP category (3) cycle II, the learning outcomes that achieve the completeness score of 25 students are 86.2% and the average value average learning outcomes 87 with high PAP category. It can be concluded that there is an increase in student learning outcomes after taking action, namely by applying the problem based learning model according to the independent curriculum.
PENENTUAN RISIKO KREDIT OBLIGASI MENGGUNAKAN MODEL KMV MERTON Safitri, Delia Ananda; Artiono, Rudianto
MATHunesa: Jurnal Ilmiah Matematika Vol. 13 No. 3 (2025)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v13n3.p595-603

Abstract

Investasi dalam instrumen obligasi memiliki potensi keuntungan yang stabil, namun juga mengandung risiko, salah satunya risiko kredit. Penelitian ini bertujuan untuk menentukan tingkat risiko kredit obligasi suatu perusahaan dengan menggunakan model KMV Merton. Model ini merupakan pendekatan struktural yang memanfaatkan data pasar seperti nilai total aset, nilai pasar ekuitas, nilai liabilitas, serta volatilitas aset perusahaan, untuk menghitung Expected Default Frequency (EDF) atau probabilitas gagal bayar. Data yang digunakan merupakan data sekunder dari perusahaan yang terdaftar di Bursa Efek Indonesia serta memiliki tingkat kredit yang baik. Adapun hasil perhitungan yang didapatkan adalah nilai volatilitas aset sebesar 0,1001509 atau 10,02%, nilai pasar ekuitas sebesar Rp 56.202.310.462.129, nilai liabilitas sebesar Rp 387.405.553.465, nilai Distance to Default (DD) sebesar 13,11908, dan nilai Expected Default Frequency (EDF) sebesar . Berdasarkan hasil tersebut menunjukkan bahwa nilai EDF perusahaan berada pada tingkat yang rendah, yang mengindikasikan bahwa risiko gagal bayar obligasi relatif kecil. Sehingga kecil kemungkinan terjadinya risiko kredit obligasi pada perusahaan. Kata Kunci: Risiko Kredit, Obligasi, KMV Merton, Expected Default Frequency (EDF), Distance to Default (DD)
Penentuan Harga Opsi Foreign Exchange Menggunakan Model Heston Stochastic Volatility Harahap, Libelda Aldinaduma; Artiono, Rudianto
MATHunesa: Jurnal Ilmiah Matematika Vol. 13 No. 3 (2025)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v13n3.p524-530

Abstract

Penelitian ini mengkaji penentuan harga opsi valuta asing USD/IDR menggunakan model Heston, yang menangkap volatilitas berubah-ubah (stokastik), dengan dua metode: transformasi Fourier dan simulasi Monte Carlo. Data nilai tukar USD/IDR periode 2020–2024 digunakan untuk analisis. Model Heston disesuaikan dengan memasukkan dua suku bunga berbeda untuk menghitung dinamika nilai tukar. Metode Fourier memberikan solusi semi-analitik yang efisien secara komputasi, sedangkan Monte Carlo menangkap dinamika stokastik melalui simulasi jalur acak. Hasil menunjukkan pola harga opsi call dan put yang konsisten terhadap nilai tukar, volatilitas, dan selisih suku bunga. Perbandingan menggunakan MAPE menunjukkan bahwa hasil keduanya relatif konsisten, terutama pada opsi put (galat <7%) dan opsi call (sekitar 14–17%). Penelitian ini memperluas penerapan model Heston dalam konteks opsi valuta asing dan menunjukkan bahwa Fourier dan Monte Carlo dapat digunakan secara saling melengkapi dalam penetapan harga derivatif.
Numerical Pricing of European Stock Options Using Black-Scholes Interval Model Aditama, Muhammad Iqbal; Artiono, Rudianto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40272

Abstract

This study presents the numerical implementation of the Black-Scholes interval model for determining the price of European call options under parameter uncertainty. Unlike the classic Black-Scholes model, which assumes fixed volatility and risk-free interest rates, this study represents both parameters as limited intervals constructed based on historical data. Daily stock closing prices obtained from Yahoo Finance and risk-free interest rate data from the Federal Reserve Bank of St. Louis were used to define the parameter ranges. The interval Black-Scholes model was discretized in the asset price and time domains and solved numerically by formulating an optimization problem that minimizes the residual error of the interval partial differential equation with terminal payoff constraints. The numerical solution produces lower and upper bounds for option prices in the specified domain. Simulation results show that classic Black-Scholes option prices lie within the calculated interval price bounds, demonstrating numerical consistency between the deterministic and interval formulations.This study provides a structured numerical case study showing how the Black-Scholes interval model can be implemented to generate option price bounds under bounded parameter uncertainty
Option Pricing Using The Partial Taylor Series Expansion Method: A Case Study of Blue-Chip Stocks on The Indonesia Stock Exchange Wijaya, Alfiano Akmal; Artiono, Rudianto
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 11 No. 1 (2026): Mathline : Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v11i1.1094

Abstract

The Indonesian capital market is characterized by dynamic stock price volatility, which directly affects the value of derivative instruments, particularly stock options. Accurate option pricing is essential for supporting investment decision-making and risk management. The Black–Scholes model is a classical and widely used framework for option pricing; however, its assumption of constant volatility often fails to reflect actual market conditions. Therefore, this study aims to apply the Partial Taylor Series Expansion (PTSE) method as an alternative approximation approach and to evaluate its accuracy relative to the analytical Black–Scholes solution. This study adopts a quantitative approach using a blue-chip stock PT. XXXX listed on the Indonesia Stock Exchange during the period 2019–2024. Model parameters are determined based on historical stock price data, the risk-free interest rate, and historical volatility. European stock option prices are calculated using both the Black–Scholes model and the PTSE method and are compared using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). In addition, sensitivity analysis is conducted to examine the effects of volatility and time to maturity on option price differences. The results indicate that the PTSE method produces option price estimates with relatively small errors and a stable convergence pattern toward the Black–Scholes model, suggesting that PTSE is a practical and efficient approximation approach for pricing European stock options in the Indonesian capital market.
Numerical Pricing of Discrete-Dividend European Options: An Empirical Case Study Elgiffary, Muhammad Gibran; Artiono, Rudianto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40995

Abstract

Studi kuantitatif terapan ini menerapkan integrasi numerik Simpson 1/3 untuk secara sistematis menerbitkan penetapan harga opsi Eropa yang disesuaikan dengan diskrit dividen. Menggunakan saham teknologi anonim (XYZ Tech Corp.) sebagai studi kasus empiris, penelitian ini mencapai dua tujuan utama: memvalidasi konvergensi komputasi algoritma numerik terhadap tolok ukur analitik Black-Scholes yang tepat menggunakan Kesalahan Relatif, dan menganalisis penyimpangan harga empiris model terhadap pengamatan pasar nyata di berbagai zona uang. Pengujian komputasi menunjukkan bahwa metode Simpson 1/3, yang secara inheren dibatasi oleh kesalahan pemotongan orde keempat, mencapai konvergensi optimal dan cepat. Dengan mengatur partisi grid pada N=200, algoritma berhasil menekan kesalahan relatif secara ketat di bawah ambang batas 0,001% dibandingkan dengan solusi analitik, dan dieksekusi secara efisien dalam waktu kurang dari 0,005 detik. Secara empiris, meskipun model teoritis menunjukkan akurasi tinggi untuk opsi In-The-Money (ITM) dengan deviasi minimal, model ini secara konsisten mengungkapkan bias valuasi yang signifikan untuk kontrak Call Out-Of-The-Money (OTM), sedangkan valuasi Put OTM menunjukkan pola deviasi yang berbeda secara struktural. Valuasi asimetri ini menunjukkan potensi batasan volatilitas historis konstan, yang tampaknya tidak mampu untuk sepenuhnya menangkap kemiringan volatilitas tersirat dan pergeseran persepsi risiko yang lazim terjadi dalam mikrostruktur pasar aktual.
Co-Authors ABADI Aditama, Muhammad Iqbal Agustin, Agil Dwi Akhiroh, Mazro’atul Asih, Findiyani Ernawati Atik Wintarti, Atik Bertha Yonata Budi Priyo Prawoto Dian Novita Dwi Juniati Elgiffary, Muhammad Gibran Fitroh, Dewi Laily Guntur Trimulyono Harahap, Libelda Aldinaduma I Ketut Budayasa Lestari, Endri Puji Maulana, Dimas Avian Mega Teguh Budiarto MUCHLIS Muhamad Arif Mahdiannur Postekoningsih, Dwi Rahaju Rachman, Kamadiyati RADEN SULAIMAN Rooselyna Ekawati Safitri, Delia Ananda Sifak Indana Taufiqi, Nuril Hidayah Ummah, Nadillatul Wasis Wasis Wijaya, Alfiano Akmal Yaqin, Mohammad Iqbal Ainul Yunianti, Dwi Nur