Marchela, Thalia Anggita (2023) Penetapan Harga European Stock Loan Dengan Metode Homotopi Perturbasi. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Saham merupakan salah satu instrumen pasar keuangan yang cukup populer. Harga saham bersifat fluktuatif sehingga terdapat banyak alternatif untuk meminimalisir risiko kerugian, seperti stock loan. Penelitian ini menggunakan asumsi pengumpulan dividen oleh lender sebelum jatuh tempo. Berdasarkan mekanismenya, stock loan memiliki kemiripan dengan call option sehingga stock loan dapat dimodelkan menggunakan persamaan diferensial Black-Scholes. Persamaan ini dapat ditransformasi menjadi persamaan difusi yang menghasilkan solusi analitik. Pada penelitian ini, persamaan diferensial Black-Scholes diselesaikan menggunakan metode Homotopi Perturbasi yang memiliki solusi berupa deret. Hasil penghitungan setiap jumlah sukunya dibandingkan dengan solusi analitik untuk menetapkan harga European stock loan. Harga stock loan dari jumlahan suku ke-4 pada solusi metode Homotopi Perturbasi mendekati solusi analitik dengan selisih yang relatif rendah. Oleh karenanya, metode Homotopi Perturbasi memiliki akurasi yang baik untuk menetapkan harga European stock loan. Harga stock loan dipengaruhi oleh tinggi rendahnya harga saham jaminan, nilai volatilitas, dan suku bunga pinjaman. Di samping itu, harga stock loan yang ditetapkan tidak akan bernilai lebih rendah dari payoff function
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Stocks are one of the most popular financial market instruments. Stock prices fluctuate so there are many alternatives to minimize the risk of loss, such as stock loan. This study uses the assumption of dividend collection by the lender before maturity. Based on the mechanism, stock loan is similar to call option so that stock loan can be modeled using the Black-Scholes differential equation. This equation can be transformed into a diffusion equation which gives an analytical solution. In this study, the Black-Scholes differential equation was also solved using the Homotopy Perturbation method which has a solution in the form of a series. The calculation results for each number of terms are compared with an analytical solution to determine the price of European stock loan. The value of stock loan from the sum of the 4th term in the solution of the Homotopy Perturbation method approaches the analytical solution with a relatively low deviation. Therefore, the Homotopy Perturbation method has good accuracy for determining European stock loan prices. The price of stock loan is affected by the fluctuation of the collateral stock’s price, the volatility value, and the loan interest rate. In addition, the set price of stock loan will not be lower than payoff function
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | Dividen, Metode Homotopi Perturbasi, Saham, Stock loan, Dividend, Homotopy Perturbation Method, Stock. |
| Subjects: | Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Thalia Anggita Marchela |
| Date Deposited: | 08 Feb 2023 09:00 |
| Last Modified: | 08 Feb 2023 09:00 |
| URI: | http://repository.its.ac.id/id/eprint/96526 |
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