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All Journal JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA Jurnal Edukasi dan Penelitian Informatika (JEPIN) Jurnal Pendidikan Informatika dan Sains Dinamisia: Jurnal Pengabdian Kepada Masyarakat JTAM (Jurnal Teori dan Aplikasi Matematika) Indiktika : Jurnal Inovasi Pendidikan Matematika Martabe : Jurnal Pengabdian Kepada Masyarakat Zero : Jurnal Sains, Matematika, dan Terapan Jurnal Nasional Pendidikan Teknik Informatika (JANAPATI) M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika Jurnal Informatika dan Rekayasa Perangkat Lunak Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Jurnal Inovasi Penelitian dan Pengabdian Masyarakat Wisanggeni : Jurnal Pengabdian Masyarakat
Chatarina Enny Murwaningtyas
Universitas Sanata Dharama
Agriculture, Biological Sciences & Forestry Arts Humanities Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Education Engineering Mathematics Physics Social Sciences Other

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Convergence and Runtime of Crank-Nicolson Schemes for Barrier Option Pricing under Mixed Fractional Brownian Motion Chatarina Enny Murwaningtyas
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 2 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i2.28088

Abstract

We examined an up-and-out barrier call under mixed fractional Brownian motion using three finite-difference time integrators: implicit Backward Euler, Crank-Nicolson (CN), and CN with a Rannacher startup. The spatial mesh was kept unchanged, while the number of time steps was increased. CN eventually produced very small price errors, but on course and moderate grids it also produced oscillations and negative values; the effect was stronger at higher volatility. Backward Euler did not show these large undershoots, although its error decreased more slowly. The Rannacher version removed the undershoots in the cases tested with little additional runtime. At N_t = 128, its relative error ranged from 8.20 x 10^-5 to 1.28 x 10^-4. For this numerical setting, the startup damping gave the most reliable moderate-grid behavior. to . 
Co-Authors Amsikan Stanislaus Andhy Rudhito, Marcellinus Andreas Ricky Proklamanto Angelin Ica Pramesti Ayuwanditya, Caecillia Berta Bete, Hendrika Binuryan, Podang Cecilia Novianti Salsinha Cyrenia Novella Krisnamurti Cyrenia Novella Krisnamurti De Jesus, Maria Fatima Dineri Evi Ervera Malau Gunawan, Monica Tiara Haniek Sri Pratini Haryono, William Saputra Hongki Julie Jeane Yosefa Tine Kristiamita, Angel Kristofel, Tedi Kuling, Oriel Lauda Feroniasanti, Yoanni Maria Lyany, Elisabeth Gunu Mahanani, Carolina Dhinda Putri Maharani, Wayan Marcellinus Andhy Rudhito Marcellinus Andy Rudhito Marfiani Tapo, Maria Monica Tiara Gunawan Niluh Sulistyani Novella Krisnamurti, Cyrenia Puspaningrum, Fibelia Dwi Putri, Agatha Lintang Antika Ika Satianingsih, Ni Made Selestina Nahak Sri Pratini, Haniek Stanislaus, Amsikan Tapo, Maria Marfiani Tiara Gunawan, Monica Tine, Jeane Yosefa Turnip, Grace Uge, Maria Andriani Yuli Listyarini, Ika