Wulandari, Ana (2018) Penerapan Metode Perturbation Pada Perhitungan Nilai Opsi Asia. Undergraduate thesis, Institut teknologi Sepuluh Nopember.
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Abstract
Metode perturbation merupakan salah satu cara untuk
menyelesaikan persamaan diferensial yang tidak dapat
diselesaikan dengan cara biasa, seperti persamaan diferensial
Black-Scholes. Pendekatan solusi model Black-Scholes
menggunakan metode perturbation menghasilkan nilai error
yang kecil terhadap solusi eksaknya. Fokus utama dalam
Tugas Akhir ini adalah penerapan metode perturbation pada
perhitungan nilai opsi Asia tipe Eropa. Opsi Asia tipe
Eropa adalah opsi dimana payo� bergantung pada rata-rata
harga aset selama opsi tersebut berlaku dan hanya dapat
dieksekusi pada saat jatuh tempo saja. Persamaan diferensial
dalam Tugas Akhir ini menggunakan persamaan diferensial
dari opsi Asia rata-rata geometrik tipe Eropa. Penerapan
metode Perturbation pada persamaan diferensial opsi Asia
rata-rata geometrik tipe Eropa melalui transformasi menjadi
persamaan difusi yang selanjutnya diberikan parameter
Perturbation sehingga didapatkan solusi. Hasil simulasi
dengan menggunakan software MATLAB menunjukkan
bahwa pengaruh parameter strike price (K), maturity date
(T), risk free interest rate (r), dan volatilitas (�) pada model opsi Asia rata-rata geometrik tipe Eropa dengan metode Perturbation sesuai dengan trend nilai opsi Asia.
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Perturbation method is a method that can be used to solve
di�erential equations that can not be solved in the usual way, such as the Black-Scholes di�erential equation. The solution
approach of Black-Scholes model is using perturbation method
yields a small error value against its exact solution. The main focus in this Final Project applied perturbation method in the calculation of value of Asian option of European type. The Asian option of the European type is an option where payo� depends on the average of asset price as long as the option is valid and can only be executed at maturity date only. The di�erential equation to be used in this Final Project is the di�erential equation of the European-Style Geometric
Average Asian Option. The application of perturbation
method to the di�erential equation of the European-Style
Geometric Average Asian Option through transformation
into a di�usion equation which is then given parameters of perturbation to obtain a solution. The results of simulation using MATLAB software shows that in
uence of strike price (K), maturity date T, risk free interest rate (r), and volatility (�) in the European-Style Geometric Average Asian Option is same with trend value of Asian Option.
Keywords: Perturbation Method, Asian Option, European
| Item Type: | Thesis (Undergraduate) |
|---|---|
| Uncontrolled Keywords: | Metode perturbation, opsi Asia, opsi Asia rata-rata geometrik tipe Eropa. |
| Subjects: | Q Science > QA Mathematics > QA278.3 Structural equation modeling. |
| Divisions: | Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Wulandari Ana |
| Date Deposited: | 09 Aug 2021 22:00 |
| Last Modified: | 09 Aug 2021 22:00 |
| URI: | http://repository.its.ac.id/id/eprint/52400 |
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