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All Journal Jurnal Ekonomi Kuantitatif Terapan dCartesian: Jurnal Matematika dan Aplikasi Jurnal Rekayasa Sistem Industri JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Abdi Insani Journal of Fundamental Mathematics and Applications (JFMA) Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya d'Cartesian: Jurnal Matematika dan Aplikasi
Leopoldus Ricky Sasongko
Universitas Kristen Satya Wacana
Agriculture, Biological Sciences & Forestry Civil Engineering, Building, Construction & Architecture Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Environmental Science Health Professions Industrial & Manufacturing Engineering Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Mathematics

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Simulation-Based Pricing and Settlement Price Distributions of Indonesian Structured Warrants Sasongko, Leopoldus Ricky; Mahatma, Tundjung; Robiyanto, Robiyanto
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29282

Abstract

The Indonesian capital market has experienced significant growth, marked by the introduction of Structured Warrants (SWs) as innovative financial instruments. This study aims to develop a robust simulation-based pricing model for Indonesian Call SWs utilizing the Geometric Brownian Motion (GBM) framework and to determine their settlement price distributions. Monte Carlo simulations were employed to accurately capture the specific characteristics of Indonesian Call SWs, notably their average-price settlement mechanism and conversion rates. The results indicate that the settlement prices conform to a lognormal distribution, validating the GBM assumption and aligning with key trading metrics such as implied volatility, which is widely utilized in the Indonesian SW market. Additionally, the Symmetrical Auto Rejection rule, which imposes realistic constraints on underlying asset price movements, significantly enhances model realism and better reflects actual market conditions. The findings reveal that simulated Indonesian Call SW prices are slightly lower compared to values derived from the Black-Scholes model adjusted for conversion rates, highlighting opportunities for further refinement of pricing methodologies. Investors can leverage these insights to better assess risks and returns by anticipating volatility and price trends, with paying close attention to conversion rates and settlement mechanisms. Issuers may benefit from improved pricing accuracy, thus minimizing mispricing risks, while regulators can utilize this research to assess current market rules and design policies aimed at increasing market efficiency and transparency. 
WORKSHOP PERSIAPAN PEMBELAJARAN MATEMATIKA DENGAN BANTUAN PAKET PROGRAM KOMPUTER (GEOGEBRA/R) UNTUK MGMP MATEMATIKA SMA KABUPATEN SEMARANG JAWA TENGAH Setiawan, Adi; Parhusip, Hanna Arini; Nugroho, Didit Budi; Sasongko, Leopoldus Ricky; Rudhito, Andy; Utomo, Beni; Fernandez, Aloysius Joakim
Jurnal Abdi Insani Vol 12 No 2 (2025): Jurnal Abdi Insani
Publisher : Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/abdiinsani.v12i2.2046

Abstract

The world is heading towards the era of Society 5.0, which requires learning Mathematics as much as possible to be easy to understand and interesting for students. Technology-based visualization, such as the use of Geogebra, can help students understand Mathematics formulas better. Therefore, teachers who are members of the High School Mathematics MGMP need to have insight into the importance of technology-based learning as a strategy to improve teaching quality. This activity aims to open teachers' insights into visualization and technology-based Mathematics learning, and help them develop creative learning modules and tools. The activity method includes four meetings consisting of webinars and workshops. The first webinar contains an introduction to the importance of visualization-based learning; the second webinar provides training in using Geogebra/R onsite or hybrid; the third webinar trains the creation of learning modules; and the fourth webinar presents the theory of writing scientific papers and using Mendeley. The results show that teachers are able to make creative and interesting lesson plans and learning modules using Geogebra/R, and motivate students to learn Mathematics independently or in groups. Some of the modules produced have been tested at school, although none of the participants have succeeded in making papers ready for publication. This activity succeeded in improving the ability of teachers to utilize technology for learning Mathematics.
The Mean Value Theorem for Integrals Method for Estimating Two-Dimensional Renewal Functions Sasongko, Leopoldus Ricky; Susanto, Bambang
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 4, No 1 (2020): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1430.842 KB) | DOI: 10.31764/jtam.v4i1.1831

Abstract

An important aspect in the provision of a two-dimensional warranty is the expected number of failures of a component during the two-dimensional warranty period. The purpose of this paper is to present a new method to obtain the expected number of failures of a nonrepairable compo­nent from the two-dimensional renewal functions as the so­lution of two-dimensional renewal integral equations through the Mean Value Theorem for Integrals (MeVTI) method. The two-dimensional renewal integral equation involves Lu-Bhattacharyya’s bivariate Weibull model as a two-dimensional failure model. It turns out that the estimation of the expected number of failures using the MeVTI method is close to that of the other method, Riemann-Stieljies method. The bivariate data behaviour of the failures of an automobile component is also studied in this paper.
Regresi Median Pada Copula Bivariat Rinadi, Geraldus Anggoro; Sasongko, Leopoldus Ricky; Susanto, Bambang
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 3, No 1 (2019): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (532.618 KB) | DOI: 10.31764/jtam.v3i1.728

Abstract

Abstrak: Analisis regresi adalah analisis yang sering digunakan dalam segala bidang yang bertujuan untuk memodelkan hubungan antara dua jenis variabel tak bebas dengan satu atau variabel bebas. Regresi linier masih memiliki beberapa kekurangan, maka dari untuk mengatasinya dengan regresi median. Copula dapat digunakan untuk mendeteksi hubungan data bivariat dengan peubah-peubah yang berbeda. Hasil penelitian menunjukkan kurva kuantil bersyarat terbaik berdasarkan MSE terkecil Data I yaitu copula Plackett sebesar 0.8650. Sedangkan nilai MSE terkecil Data II yaitu copula Gaussian sebesar 0.3954. Nilai MSE terkecil Data III yaitu copula Frank sebesar 0.5575. Terakhir, nilai MSE terkecil Data IV yaitu copula Clayton sebesar 0.3190.Abstract:  Regression analysis is an analysis that is often used in all fields which aims to model the relationship between two types of non-dependent variables with one or independent variables. Linear regression still has several drawbacks, so to overcome this by median regression. Copula can be used to detect bivariate data relations with different variables. The results showed that the best conditional curves based on the smallest MSE of Data I were Plackett copula of 0.8650. While the smallest MSE value is Data II, which is a Gaussian population of 0.3954. The smallest MSE value of Data III is Frank copula of 0.5575. Finally, the smallest MSE value is Data IV which is copula Clayton of 0.3190.
GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH Models Nugroho, Didit Budi; Panjaitan, Lam Peter; Kurniawati, Dini; Kholil, Zaini; Susanto, Bambang; Sasongko, Leopoldus Ricky
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 2 (2022): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i2.7694

Abstract

Numerous variants of the basic Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have been proposed to provide good volatility estimating and forecasting. Most of the study does not work Excel’s Solver to estimate GARCH-type models. The first purpose of this study is to provide the capability analyze of the GRG non-linear method built in Excel’s Solver to estimate the GARCH models in comparison to the adaptive random walk Metropolis method in Matlab by own codes. The second contribution of this study is to evaluate some characteristics and performance of the GARCH-M(1,1), GJR(1,1), and log-GARCH(1,1) models with Normal and Student-t error distributions that fitted to financial data. Empirical analyze is based on the application of models and methods to the DJIA, S&P500, and S&P CNX Nifty stock indices. The first empirical result showed that Excel’s Solver’s Generalized Reduced Gradient (GRG) non-linear method has capability to estimate the econometric models. Second, the GJR(1,1) models provide the best fitting, followed by the GARCH-M(1,1), GARCH(1,1), and log-GARCH(1,1) models. This study concludes that Excel’s Solver’s GRG non-linear can be recommended to the practitioners that do not have enough knowledge in the programming language in order to estimate the econometrics models. It also suggests to incorporate a risk premium in the return equation and an asymmetric effect in the variance equation. 
Co-Authors A.A. Ketut Agung Cahyawan W Adi Setiawan Aditya Toraismaya ALOYSIUS JOAKIM FERNANDEZ Anggita M Kusumawati Arisandi, Nia Lestari Bambang Susanto Beni Utomo David Elsa Kharisma Dewi Lukitasari Didit Budi Nugroho Dini Kurniawati Egidius Saut Poltak Situmorang Ferdy Semuel Rondonuwu Fitri, Nirmala Ayu Andika Hanna Arini Parhusip Hariyanto, H Indah Kristin Utami Jaja, Visher Laja Kholil, Zaini Laurentia Nindya Sari Prameswara Lilik Linawati Nur Rohman Panjaitan, Lam Peter Prameswara, Laurentia Nindya Sari Putri, Lauria Ineke Rika Listiyani Rinadi, Geraldus Anggoro Robiyanto Robiyanto, Robiyanto Rudhito, Andy Saputri, Selvina Merry Situmorang, Egidius Saut Poltak Tundjung Mahatma Visher Laja Jaja Yusuf Kurniawan