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All Journal Sewagati Indonesian Journal of Applied Mathematics
Hakam, Amirul
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Arts Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Languange, Linguistic, Communication & Media Physics Public Health Social Sciences Other

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An Alternative Derivation of the Black-Sholes Model for Option Pricing Hakam, Amirul; Savira, Dhea Rahma; Putri, Endah RM
Indonesian Journal of Applied Mathematics Vol. 5 No. 2 (2025): Indonesian Journal of Applied Mathematics Vol. 5 No. 2 October Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v5i2.2433

Abstract

Investment enables investors to acquire shares in capital markets or their derivative assets, with options being one of the most common instruments. An option is a contract granting the right to buy or sell an underlying asset under specific conditions. The Black–Scholes equation is widely used for option pricing, though its derivation through Backward Stochastic Differential Equations (BSDEs) is less common. BSDEs are particularly relevant in incomplete markets, where not all options can be perfectly replicated. BSDEs also avoid the need to transform probability measures into the risk-neutral, thereby simplifying the pricing procedure. This study derives the Black–Scholes equation via BSDEs, modeling investor wealth and applying the Feynman–Kac theorem. The solution for call options is obtained by transforming the variables to get a diffusion equation, while put option prices are derived using the put–call parity principle. Finally, simulations of the Black–Scholes formula are conducted to analyze option price behavior under varying volatility and risk-free interest rates.
Penguatan Kompetensi Analitik dalam Layanan Publik di PT Jasamarga Transjawa Tol, Satelit-Surabaya Valeriana, Valeriana Lukitosari; Surjanto, Sentot Didik; Wardhani, Laksmi Prita; Putri, Endah Rokhmati Merdika; Safarina, Sena; Hakam, Amirul; Fadhilah, Helisyah Nur; Nabila, Galuh Putri; Nurviana, Asyira; Pratama, Fajar Wahyu; PL, Valentinus
Sewagati Vol 10 No 2 (2026): pre printed
Publisher : Pusat Publikasi ITS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j26139960.v10i2.8955

Abstract

Kemampuan analitik menjadi elemen penting dalam penguatan mutu layanan publik di era berbasis data. Pada sektor transportasi jalan tol, analisis yang tepat terhadap pendapatan, volume kendaraan, dan dinamika spasial wilayah berperan besar dalam menjaga kinerja operasional dan kepuasan pengguna. Kegiatan pengabdian masyarakat ini dilaksanakan sebagai sharing session antara tim akademik dari Matematika, Institut Teknologi Sepuluh Nopember (ITS) dan PT Jasamarga Transjawa Tol, Satelit–Surabaya. Kegiatan ini bertujuan mengenalkan teori, aplikasi, dan manfaat analisis peramalan dan spasial dalam konteks pengelolaan layanan publik. Model Autoregressive Integrated Moving Average (ARIMA) dibahas sebagai pendekatan untuk memprediksi pendapatan tol, sedangkan Generalized Space-Time Autoregressive (GSTAR) digunakan untuk memahami pola volume kendaraan antar gerbang tol. Selain itu, Geographically Weighted Negative Binomial Regression (GWNBR) dikenalkan untuk menganalisis pengaruh faktor spasial terhadap pembukaan lahan di sekitar akses tol. Pihak Jasamarga turut berbagi pengalaman mengenai kondisi lapangan, tantangan operasional, dan kejadian-kejadian yang memengaruhi kinerja layanan. Kegiatan ini memperkuat kolaborasi antara akademisi dan praktisi industri serta memberikan pemahaman bersama tentang potensi penerapan analisis data dalam peningkatan mutu layanan publik.
Co-Authors Helisyah Nur Fadhilah Nabila, Galuh Putri Nurviana, Asyira PL, Valentinus Pratama, Fajar Wahyu Putri, Endah RM Putri, Endah Rokhmati Merdika Safarina, Sena Savira, Dhea Rahma Sentot Didik Surjanto Valeriana, Valeriana Lukitosari Wardhani, Laksmi Prita