Amansa, Ritsy (2019) Metode Prediktor Korektor Untuk Persamaan Diferensial Stock Loan Dan Opsi Beli Amerika. Sarjana thesis, Universitas Brawijaya.
Abstract
Stock loan adalah kontrak yang melibatkan dua pihak yaitu peminjam dan pemberi pinjaman dengan saham sebagai jaminan. Kontrak stock loan memiliki kemiripan mekanisme seperti pada kontrak Opsi Beli Amerika sehingga sistem persamaan stock loan dapat mengadopsi sistem persamaan Opsi Beli Amerika. Meskipun memiliki mekanisme yang sama, keduanya memiliki perbedaan yaitu pada Stock Loan terdapat bunga pinjaman, sementara itu pada Opsi Beli Amerika tidak ada suku bunga pinjaman. Pada skripsi ini, persamaan diferensial Stock Loan dan Opsi Beli Amerika diperoleh menggunakan analisis portofolio, Lemma Ito dan Proses Wiener. Kondisi batas diperoleh dari analisis matematika pada bidang finansial. Setelah didapatkan sistem persamaan diferensial Stock Loan dan Opsi Beli Amerika, dilakukan transformasi sistem persamaan agar lebih sederhana untuk diterapkan ke skema numerik. Setelah itu dilakukan simulasi numerik pengaruh perubahan beberapa variabel pada sistem persamaan diferensial menggunakan Metode Prediktor Korektor. Skema Prediktor menggunakan metode eksplisit dan skema Korektor menggunakan metode implisit. Simulasi numerik dilakukan dengan bantuan software MATLAB.
English Abstract
Stock loan is a contract between two parties, they are the borrower and the lender with stock as the collateral. The stock loan contract has a similar mechanism with American Call Option so that the stock loan equation system can adopt the equation system of American Call Options. Even though they have the same mechanism, both of them have differences. There are loan interest rates in the Stock Loan contract , while in American Call Option there are no loan interest rates. In this paper, the forming of differential equations of Stock Loan and American Call Options using portfolio analysis, Lemma Ito and Wiener Process. Boundary conditions are obtained from mathematical analysis in the financial field. After that, a transformation of system equation is carried out to apply for numerical schemes. Numerical simulation was carried out by influencing changes in several variables in the differential equation system using the Predictor Corrector Method. Predictor Schemes use explicit methods and the Corrector scheme uses implicit methods. The numerical Simulation is done with MATLAB software.
Other obstract
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| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2019/39/051910741 |
| Uncontrolled Keywords: | Stock Loan, Opsi Beli Amerika, Metode Prediktor Korektor. Stock Loan, American Call Option, Predictor Corrector Method. |
| Subjects: | 500 Natural sciences and mathematics > 515 Analysis > 515.3 Differential calculus and equations |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Budi Wahyono Wahyono |
| Date Deposited: | 24 Aug 2020 07:33 |
| Last Modified: | 29 Mar 2022 02:11 |
| URI: | http://repository.ub.ac.id/id/eprint/176754 |
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