Pratama, Arfian Rizky Satria (2022) Penerapan Metode Homotopi Perturbasi Sebagai Pendekatan Harga Maksimum Rainbow Option. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Opsi pelangi (rainbow option) merupakan jenis opsi eksotik yang nilainya bergantung pada dua atau lebih aset dasar. Penentuan harga opsi pelangi seringkali melibatkan evaluasi integral berdimensi tinggi yang kompleks, sehingga memerlukan pendekatan numerik atau analitik. Pada penelitian ini, metode homotopi perturbasi (HPM) diterapkan untuk mengestimasi harga opsi pelangi tipe maksimum (maximum rainbow option) dengan dua aset. Metode homotopi perturbasi merupakan metode yang menggabungkan teknik homotopi dan perturbasi untuk menyelesaikan persamaan diferensial. Hasil perhitungan menggunakan metode homotopi perturbasi kemudian dibandingkan dengan metode Black-Scholes untuk opsi pelangi. Berdasarkan hasil simulasi, metode homotopi perturbasi memberikan hasil estimasi harga opsi yang cukup akurat dan efisien dibandingkan dengan metode analitik yang ada.
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Rainbow options are a type of exotic option whose value depends on two or more underlying assets. Pricing rainbow options often involves complex high-dimensional integral evaluations, thus requiring numerical or analytical approaches. In this study, the homotopy perturbation method (HPM) is applied to estimate the price of maximum rainbow options with two assets. The homotopy perturbation method is a technique that combines homotopy and perturbation techniques to solve differential equations. The calculation results using the homotopy perturbation method are then compared with the Black-Scholes method for rainbow options. Based on the simulation results, the homotopy perturbation method provides quite accurate and efficient option price estimation results compared to existing analytical methods.
| Item Type: | Thesis (Other) |
|---|---|
| Additional Information: | RSMa 511.8 Pra p-1 2022 |
| Uncontrolled Keywords: | Opsi pelangi. Metode homotopi perturbasi. Rainbow option. Homotopy perturbation method. |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Mr. Marsudiyana - |
| Date Deposited: | 08 Jun 2026 03:18 |
| Last Modified: | 08 Jun 2026 03:18 |
| URI: | http://repository.its.ac.id/id/eprint/133623 |
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