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All Journal Jurnal Sains dan Seni ITS International Journal of Computing Science and Applied Mathematics
Hakam, Amirul
Department Of Mathematics Institut Teknologi Sepuluh Nopember
Arts Humanities Computer Science & IT Education Mathematics

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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.
Digital Option Pricing Approach Using A Homotopy Perturbation Method Amirul Hakam; Islachiyatul Ummah; Frida Akbar Rani; Nur Asiyah; Endah RM Putri
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 7, No 2 (2021)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.v7i2.9776

Abstract

An option is a financial contract between buyers and sellers. The Black-Scholes equation is the most popular mathematical equation used to analyze the option pricing. The exact solution of the Black-Scholes equation can be approached by several approximation methods, one of the method is a Homotopy Perturbation Method (HPM). The simplest type of option, digital options were analyzed using the HPM. The digital option pricing approach using the HPM is in a power series form, which in this paper is presented the solution in the fourth power. This solution is compared with the exact solution of the Black-Scholes equation for digital options. The results show that the approach using HPM is very accurate.
Numerical Simulation of Fluid Flow Around Circular Cylinder and Three Passive Controls to Reduce Drag Coefficient at Re=500 Chairul Imron; Amirul Hakam; Basuki Widodo; Tri Yogi Yuwono
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 6, No 1 (2020)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (739.569 KB) | DOI: 10.12962/j24775401.v6i1.5331

Abstract

Numerical experiments and simulations of fluid flow through the outer surface of a circular cylinder and three passive controls have been investigated to determine the proper configuration of three passive controls in reducing the drag coefficient. One of passive controls is placed in front of the cylinder with distance ratio (S:D) = 2:4 and the other two passive controls are placed behind the cylinder with distance ratio (T:D) = 1:6;1:8. The angle between two passive controls behind the cylinder are a =30 deg;60 deg;90 deg;120 deg. The Navier-Stokes equations for incompressible, viscous and unsteady fluid flows is solved based on SIMPLE (Semi-Implicit for Pressure-Linked Equations) algorithms and discretized using finite-difference method. The difference in a affects the reduction in the drag coefficient significantly. The best configuration of three passive controls design is one of passive controls put at the distance ratio S=D = 2:4;T=D = 1:6 and a = 60. This configuration can reduce the drag coefficient optimally to 21.2109%.
Penerapan Metode Kalman Filter dalam Estimasi Harga Saham Menggunakan Model ARCH-GARCH Lusi Nur Rahmawati; Mardlijah Mardlijah; Amirul Hakam
Jurnal Sains dan Seni ITS Vol 12, No 1 (2023)
Publisher : Lembaga Penelitian dan Pengabdian Kepada Masyarakat (LPPM), ITS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j23373520.v12i1.96240

Abstract

Saham merupakan produk pasar modal yang menjadi salah satu instrumen investasi. Banyak investor yang memilih saham sebagai instrumen investasi dikarenakan saham memberikan keuntungan yang menarik. Metode estimasi merupakan metode yang tepat bagi para investor untuk memprediksi harga saham sehingga dapat membantu mengoptimalkan keuntungannya. Penelitian ini bertujuan untuk menentukan model terbaik dari data harga saham menggunakan model ARCH-GARCH dan mendapatkan hasil estimasi harga saham menggunakan metode Kalman Filter dengan model ARCH-GARCH untuk periode selanjutnya. Adapun data harga saham yang digunakan yaitu data harga saham PT. Telkom Indonesia Tbk yang diambil dari website resmi Yahoo Finance. Data yang diambil adalah data harga saham saat penutupan (close) periode 29 Februari 2020 sampai 31 Agustus 2021. Pada data harga saham digunakan model ARIMA (Autoregressive Integrated Moving Average) dan terdeteksi terdapat unsur heteroskedastisitas, sehingga digunakan model time series ARCH-GARCH (Autoregressive Conditional Heteroskedasticity Generalized Autoregressive Conditional Heteroskedasticity). Didapatkan model terbaik yaitu GARCH (1,1) dengan model ARIMA (2,1,3). Pada penerapan metode Kalman Filter didapatkan hasil estimasi harga saham lebih akurat yaitu mendekati data aktual yang ditandai dengan nilai MAPE (Mean Absolute Percentage Error) pada GARCH-Kalman Filter lebih kecil dibandingkan nilai MAPE pada model GARCH (1,1).
Co-Authors Basuki Widodo Chairul Imron, Chairul Endah RM Putri Endah Rokhmati Merdika Putri Frida Akbar Rani Islachiyatul Ummah Lusi Nur Rahmawati Mardianto, Lutfi Mardlijah - Nur Asiyah Pratama, Aditya Putra Soemarsono, Annisa Rahmita Triyogi Yuwono