PENERAPAN TRANSFORMASI FOURIER PADA PENENTUAN HARGA AMERICAN DOWN-AND-OUT CALL OPTION

MASHITASARI, DEWI (2017) PENERAPAN TRANSFORMASI FOURIER PADA PENENTUAN HARGA AMERICAN DOWN-AND-OUT CALL OPTION. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Salah satu metode untuk mendapatkan penyelesaian closed-form dari American option adalah dengan menggunakan Transformasi Fourier. Diantara penelitian-penelitian yang sudah dilakukan, terdapat tiga metode yang dapat dibentuk dengan menggunakan Transformasi Fourier, yaitu metode McKean, metode Kim, dan metode Carr, Jarrow dan Myneni, dengan hasil berupa penyelesaian closed-form dalam bentuk integral. Penelitian ini meneruskan penggunaan Transformasi Fourier untuk mendapatkan penyelesaian closed-form(penyelesaian analitik) dari American Down-and-Out Call Option berdasarkan metode McKean. Setelah dilakukan tahapan penelitian, didapatkan penyelesaian analitik dari American Down-and-Out Call Option. Dari penyelesaian analitik tersebut, dilakukan simulasi numerik untuk mendapatkan gambaran secara umum dari profit American Down-and-Out Call Option. Gambaran umum dari profit tersebut menunjukkan bahwa American Down- and-OutCall Option dengan rebate sama dengan 0 memiliki pola yang sama dengan pay off function dari American Call Option. ==================================================================================================== One of the method to get closed-form solution from American option is using Fourier transform. Among the current research, three methods using Fourier transform, are McKean method, Kim method, and Carr, Jarrow, and Myneni method, which has closed-form solution in integral form. This research extend the use of Fourier transform to find and describe the analytic closed-form solution of American Down-and-Out Call Option based on McKean method. After the stages of research, analytical solution obtained from the American Down-and-Out Call Option. From the completion of the analytical, numerical simulations conducted to get a general overview of profit American Down-and-Out Call Option. An overview of the profit shows that the American Down-and-OutCall Option with a rebate equal to 0 has the same pattern with the payoff function of American Call Option.

Item Type: Thesis (Masters)
Uncontrolled Keywords: American call option, Barrier Down-and-Out option, Fourier transform
Subjects: Q Science
Q Science > QA Mathematics
Q Science > QA Mathematics > QA404 Fourier series
Divisions: Faculty of Mathematics and Science > Mathematics > (S2) Master Theses
Depositing User: DEWI MASHITASARI
Date Deposited: 30 Jan 2017 04:32
Last Modified: 30 Jan 2017 04:32
URI: http://repository.its.ac.id/id/eprint/2452

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