Metode Homotopi Perturbasi Untuk Penetapan Harga Opsi Call Spread

Maria, Roito Angelina. R (2023) Metode Homotopi Perturbasi Untuk Penetapan Harga Opsi Call Spread. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Derivatif adalah sebuah instrumen investasi yang nilainya tergantung pada nilai dari aset yang mendasarinya. Salah satu contoh produk derivatif adalah opsi. Opsi adalah kontrak keuangan yang memberikan pemegang hak, tetapi bukan kewajiban untuk membeli atau menjual suatu aset pada harga dan dalam jangka waktu tertentu. Berdasarkan haknya, terdapat dua jenis opsi, yaitu opsi call dan opsi put. Berdasarkan periode pelaksanaannya, opsi dibagi menjadi opsi tipe Amerika dan opsi tipe Eropa. Salah satu jenis opsi, yaitu opsi call spread. Opsi call spread merupakan opsi yang memperoleh nilai dari selisih antara harga dari 2 (dua) atau lebih aset dan harga kesepakatannya. Pada penelitian tugas akhir ini, dibahas metode homotopi perturbasi untuk menentukan harga opsi call spread. Persamaan Black-Scholes ditransformasikan ke bentuk non dimensional, kemudian diselesaikan menggunakan persamaan difusi untuk mendapatkan solusi analitik, dan metode homotopi perturbasi untuk mendapatkan pendekatan solusi analitik yang berupa deret. Harga opsi call spread yang diperoleh menggunakan solusi analitik dan metode homotopi perturbasi dibandingkan untuk menganalisis akurasi dari metode homotopi perturbasi dalam menetapkan harga opsi call spread. Harga opsi call spread yang diperoleh menggunakan solusi metode homotopi perturbasi untuk penjumlahan deret hingga suku ke-10 mendekati solusi analitik dengan selisih yang relatif rendah. Dengan demikian, metode homotopi perturbasi dinilai memiliki akurasi yang baik dalam menetapkan harga opsi call spread. Dilakukan pula simulasi harga opsi call spread untuk beberapa nilai parameter yang berbeda. Hasil simulasi menunjukkan bahwa harga opsi call spread dipengaruhi oleh harga saham dan nilai volatilitas.
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Derivatives are investment instruments whose value depends on the value of the underlying assets. One example of a derivative product is an option. An option is a financial contract that gives the holder the right, but not the obligation, to buy or sell an asset at a specified price within a certain period of time. Based on their rights, options can be divided into two types: call options and put options. Based on their exercise period, options are classified into American options and European options. One type of option is a call spread option. A call spread option derives its value from the difference between the prices of two or more assets and its strike price. In this final project research, the homotopy perturbation method is discussed to determine the price of a call spread option. The Black-Scholes equation is transformed into a non-dimensional form, then solved using the diffusion equation to obtain an analytical solution, and the homotopy perturbation method is used to obtain an approximate analytical solution in a series form. The prices of the call spread option obtained using the analytical solution and the homotopy perturbation method are compared to analyze the accuracy of the homotopy perturbation method in determining the price of the call spread option. The price of the call spread option obtained using the homotopy perturbation method with the summation of the series up to the 10th term approximates the analytical solution with a relatively small difference. Thus, the homotopy perturbation method is considered to have good accuracy in determining the price of the call spread option. Simulation of the call spread option prices is also conducted for various parameter values. The simulation results show that the price of the call spread option is influenced by the stock price and the volatility value.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Opsi Call Spread, Persamaan Black-Scholes, Metode Homotopi Perturbasi, Call Spread Option, Black-Scholes Equation, Homotopy Perturbation Method
Subjects:	H Social Sciences > HG Finance H Social Sciences > HJ Public Finance
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Maria Roito Angelina R
Date Deposited:	07 Aug 2023 02:22
Last Modified:	07 Aug 2023 02:32
URI:	http://repository.its.ac.id/id/eprint/103120

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