Penentuan Harga Opsi Asia Aritmatika Menggunakan Metode Perturbasi

Anshori, Faizin (2018) Penentuan Harga Opsi Asia Aritmatika Menggunakan Metode Perturbasi. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Opsi Asia merupakan salah satu jenis opsi non-standart yang payo�-nya bergantung pada rata-rata harga aset. Pada penentuan harga opsi Asia dibentuk suatu model opsi Asia. Model opsi Asia didapatkan berdasarkan pembentukan portfolio dengan menerapkan formula It�o, delta hedging dan prinsip free of arbitrage. Pada penelitian ini, rata-rata harga aset yang digunakan adalah jenis rata-rata aritmatika dan rata-rata aritmatika tidak diketahui jenis distribusinya. Untuk model opsi Asia dengan rata-rata aritmatika belum ditemukan solusi analitiknya. Sehingga, perlu digunakan aproksimasi. Aproksimasi yang diterapkan adalah metode perturbasi. Penerapan metode perturbasi pada model opsi Asia aritmatika melalui transformasi model menjadi persamaan difusi yang selanjutnya diberikan parameter perturbasi dan barisan asimtotis, sehingga didapatkan suatu solusi. Solusi yang dihasilkan berupa solusi konvergen dengan akurasi yang sangat baik (MAPE kurang dari 10 %). ============================================================ The Asian option is one of the non-standard options whose payo� depends on the average asset price. In pricing Asia option established an Asian option model. The Asian option model is based on the formation of a portfolio by applying the It�o formula, delta hedging, and free of arbitrage principle. In this study, the average price of assets used by the type is the average of arithmetic and the average of arithmetic is not known the type of distribution. For Asian option model with arithmetic mean has not been found its analytical solution. Therefore, an approximation is required. The approximation applied is perturbation method. The application of the perturbation method to the Asian arithmetic option model through model transformation into a di�usion equation which is then given parameters of perturbation and sequence of asymptotes, to obtain a solution. The resulting solution is a convergent with excellent accuracy (MAPE less than 10 %).

Item Type: Thesis (Undergraduate)
Uncontrolled Keywords: Opsi Asia, Rata-rata aritmatika, Metode perturbasi
Subjects: Q Science > QA Mathematics > QA274.7 Markov processes--Mathematical models.
Divisions: Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User: FAIZIN ANSHORI
Date Deposited: 28 Jun 2021 03:07
Last Modified: 28 Jun 2021 03:07
URI: https://repository.its.ac.id/id/eprint/55688

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