Penentuan Harga Digital Call Option dengan Model Black-Scholes Menggunakan Metode Homotopi Perturbasi

Ummah, Islachiyatul (2020) Penentuan Harga Digital Call Option dengan Model Black-Scholes Menggunakan Metode Homotopi Perturbasi. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Opsi merupakan suatu produk investasi yang nilainya bergantung pada harga saham. Sayangnya pergerakan harga saham di pasar modal cenderung tidak stabil dan susah untuk diprediksi. Penelitian ini bertujuan untuk menentukan harga opsi call digital dengan model Black-Scholes menggunakan dua metode dan untuk mengetahui kinerja metode tersebut. Pertama, solusi analitik dari model Black-Scholes dicari dengan mengubahnya menjadi persamaan difusi. Kemudian, solusi pendekatan analitiknya dicari menggunakan metode homotopi perturbasi. Setelah itu, dilakukan simulasi dengan membandingkan kedua nilai tersebut. Hasil yang didapatkan adalah nilai dari solusi pendekatan analitik mendekati nilai dari solusi analitik. Jadi, dapat disimpulkan bahwa metode homotopi perturbasi dapat digunakan untuk mencari solusi pendekatan analitik model Black-Scholes dan menghasilkan solusi pendekatan yang cukup akurat. ================================================================================================================= Option is a derivative investment product whose value depends on the stock price. Unfortunately, the stock price fluctuating and difficult to predict. In this paper, we discuss how to determine the price of digital call options with the Black-Scholes model using two methods and to determine the accuracy of these methods. First, the analytical solution is sought by transforming it into a diffusion equation. Then, the approximate analytical solution is sought using the homotopy perturbation method. After getting the analytical solution and approximate analytical solution for Black-Scholes then simulating it to compare the values. It's concluded that the approximate analytical solution obtained using homotopy perturbation method approaches the value of the analytical solution. So, homotopy perturbation method can be used to find the approximate analytical solution for Black-Scholes model and generate an accurate approximate solution.

Item Type: Thesis (Undergraduate)
Uncontrolled Keywords: Metode Homotopi Perturbasi, Model Black-Scholes, Opsi, Opsi Digital. Black-Scholes Model, Digital Call Option, Homotopy Perturbation Method, Option.
Subjects: H Social Sciences > HG Finance > HG4012 Mathematical models
Divisions: Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User: Islachiyatul Ummah
Date Deposited: 27 Aug 2020 02:05
Last Modified: 27 Aug 2020 02:05
URI: https://repository.its.ac.id/id/eprint/79748

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