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All Journal Journal of Science and Applicative Technology Limits: Journal of Mathematics and Its Applications International Journal of Computing Science and Applied Mathematics Jurnal Matematika UNAND Indonesian Journal of Applied Mathematics
Mardianto, Lutfi
Program Studi Matematika Institut Teknologi Sumatera, Lampung Selatan, 35365, Indonesia
Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics

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Comparison of Numerical Methods on Pricing of European Put Options Mardianto, Lutfi; Pratama, Aditya Putra; Soemarsono, Annisa Rahmita; Hakam, Amirul; Putri, Endah Rokhmati Merdika
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 5, No 1 (2019)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (170.702 KB) | DOI: 10.12962/j24775401.v5i1.3172

Abstract

Put option is a contract to sell some underlying assets in the future with a certain price. On European put options, selling only can be exercised at maturity date. Behavior of European put options price can be modeled by using the Black-Scholes model which provide an analytical solution. Numerical approximation such as binomial tree, explicit and implicit finite difference methods also can be used to solve Black-Scholes model. Some numerical methods are applied and compared with the analytical solution to determine the best numerical method. The results show that numerical approximations using the binomial tree is more accurate than explicit and implicit finite difference method in pricing European put options. Moreover when the value of T is higher then the error obtained is also higher, while the error obtained is lower when the value of N is higher. The value of T and N cause the increase of the computation time. When the value of T is higher the computation time is lower, while computation time is higher if the value of N is higher. Overall, the lowest computation time is obtained by using an explicit finite difference method with an exceptional as the value of T is big and the value of N is small. The lowest computation time is obtained by using a binomial tree method.
Aliran Konveksi Campuran Magnetohidrodinamik yang Melewati Bola Bermagnet Lutfi Mardianto; Basuki Widodo; Dieky Adzkiya
Limits: Journal of Mathematics and Its Applications Vol 17, No 1 (2020)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v17i1.6752

Abstract

Permasalahan yang dibahas pada paper ini adalah aliran konveksi campuran magnetohidrodinamik (MHD) tak tunak dari fluida Newtonian yang melalui bola bermagnet. Persamaan pembangun dimensional terdiri dari persamaan kontinuitas, persamaan momentum dan persamaan energi. Persamaan ini diubah ke bentuk non-dimensional menggunakan variabel non-dimensional. Selnajutnya, semua persamaan dianalisis dengan teori lapisan batas dan ditransformasikan ke bentuk persamaan non-similar. Persamaan ini diselesaikan secara numerik menggunakan metode beda hingga skema implisit. Profil kecepatan dan temperatur di permukaan bola bermagnet ditentukan oleh beberapa parameter seperti bilangan Prandtl (Pr), parameter magnetik (M) dan parameter konveksi campuran (α). Gesekan kulit dan transfer panas dipelajari dan diinvestigasi selain kecepatan dan temperatur.
Distribusi spasial kualitas perairan dan hubungannya dengan aktifitas budidaya perikanan di Teluk Lampung Budhi Agung Prasetyo; Muawanah Muawanah; Lutfi Mardianto; Muhammad Zainuddin Lubis
Journal of Science and Applicative Technology Vol 6 No 1 (2022): Journal of Science and Applicative Technology June 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/jsat.v6i1.897

Abstract

Coastal water is water areas that receive much input of organic matter originating from human activities on land. Anthropogenic activities such as marine aquaculture in Teluk Lampung impact water quality on that waters. This study was conducted to determine the distribution of water quality around Teluk Lampung and its correlations to marine aquaculture activities. The analysis carried out in this study is spatial analysis to determine the spatial distribution of water quality in three focus area, namely Teluk Hurun (HB), Selatan Teluk Hurun (SHB) dan Pantai Sari Ringgung (SRB) as part of Teluk Lampung. In addition to spatial analysis, principal component analysis (PCA) was also carried out to determine water quality as a variable and its correlation to each area. Based on the results of this study, the spatial distribution of water quality varies based on the human activities type in each area. Based on the results of principal component analysis, it is known that the variability of several water quality variables also correlates with the human activities types, such as marine aquaculture and beach tourism.
Metode Runge-Kutta Orde 4 Dalam Penyelesaian Persamaan Gelombang 1D Syarat Batas Dirichlet Yenci Brika Enkekes; Lutfi Mardianto
Indonesian Journal of Applied Mathematics Vol 2 No 1 (2022): Indonesian Journal of Applied Mathematics Vol. 2 No. 1 April 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.v2i1.489

Abstract

The problem studied in this study was the movement of deviations in the equation of 1D waves on the rope given the initial deviation value. In this study, the equation of 1D waves with dirichlet boundary problems will be solved analytically using variable and numerical separation using the runge-kutta method approach of order 4. This research begins with examining equation models, solving analytical solutions, applying schemes to the final results of simulations. The decrease in equation model fissile is done by reviewing the working force on a piece of rope, solving an analytical solution with a variable separation method, and numerical completion resulting in the best simulation result with parameter c= 0.5 with time steps ∆x= 0.01 and time interval of 0 ≤ t≤ 1 resulting in a numerical approach close to its analytical solution up to t= 1 s and the influence of parameter c on the movement of wave deviations resulted in that the influence of parameter c affects the magnitude of the deviation of the wave, so the greater the value of parameter c, the smaller deviation of the wave and the faster the speed of the direction. Thus, it can be concluded that the runge-kutta method of order 4 in this study can be said to be one of the numerical approaches of the problem of 1D wave equations with dirichlet boundaries.
Analisis Sistem Antrian pada Pelayanan Help Desk UPT TIK Institut Teknologi Sumatera Menggunakan Teori Antrian Dwi Rianti; Utriweni Mukhaiyar; Lutfi Mardianto
Indonesian Journal of Applied Mathematics Vol 2 No 1 (2022): Indonesian Journal of Applied Mathematics Vol. 2 No. 1 April 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.v2i1.534

Abstract

The analysis of the queuing system at the Help Desk service of the UPT TIK Institut Teknologi Sumatera includes the number of ticket arrivals, the average length of service time, and the number of service facilities (admin). The data for the number of Help Desk tickets are Poisson distributed and the service time is the Exponential distribution. The size of the steady-state in the service has a value of so that an analysis of the performance size of the queue system can be carried out. The data used in the study are Help Desk ticket data for the period November 2020-February 2021. The results obtained indicate that the queue model for the Help Desk service can be added to the server (admin). The addition of a server in the service can reduce the workload significantly. The queue model that can be applied is M/M/3:FCFS/∞/∞ by adding one server (admin), from the previous model, namely M/M/2:FCFS/∞/∞.
Numerical Solution of European Put Option for Black-Scholes Model Using Keller Box Method Lutfi Mardianto; Gusrian Putra; Benediktus Ivan Pratama; Endah R. M. Putri
Jurnal Matematika UNAND Vol 13, No 3 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.3.188-197.2024

Abstract

In this study, we propose to determine option pricing by using Black-Scholes model numerically. The Keller box method, a numerical method with a box-shaped implicit scheme, is chosen to solve the problem of pricing stock options, especially European-put option. This option pricing involves several parameters such as stock price volatility, risk-free interest rate and strike price. The numerical stability of the method is checked using Von Neumann stability before the simulation is conducted. The influence of interest rates, volatility, and strike price on the option price state that the higher the value of the interest rate parameter, the lower the option price value, while the greater the value of stock price volatility and strike price, the higher the option price.
Co-Authors Basuki Widodo Benediktus Ivan Pratama Budhi Agung Prasetyo Dieky Adzkiya Dwi Rianti Endah R. M. Putri Endah Rokhmati Merdika Putri Gusrian Putra Hakam, Amirul Muawanah Muawanah Muhammad Zainuddin Lubis Pratama, Aditya Putra Soemarsono, Annisa Rahmita Utriweni Mukhaiyar Yenci Brika Enkekes