Penyelesaian Model Black-Scholes Pada American Stock Loan Menggunakan Transformasi Laplace

Anggraini, Silda Sari (2023) Penyelesaian Model Black-Scholes Pada American Stock Loan Menggunakan Transformasi Laplace. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Stock loan adalah kontrak perjanjian yang melibatkan dua pihak yakni lender sebagai pemberi pinjaman dan borrower sebagai peminjam dengan jaminan saham. Mekanisme pelaksanaan stock loan hampir sama dengan American call option. Oleh karena itu, stock loan dapat diselesaikan dengan model Black-Scholes yang mengikuti Geometric Brownian Motion. Model tersebut dapat ditransformasi ke dalam bentuk non dimensional untuk menjadi model yang lebih sederhana. Selanjutnya model diselesaikan dengan menggunakan transformasi Laplace. Solusi yang diberikan berupa solusi semi analitik karena inversnya menggunakan numerical Laplace inversion dengan metode Stehfest. Dalam perhitungannya didapat nilai optimal exit price semakin meningkat seiring bertambahnya waktu jatuh tempo. Hal ini berbanding lurus dengan nilai American stock loan yang telah didapat. Diketahui bahwa semakin tinggi harga saham dan lamanya masa kontrak maka semakin tinggi pula nilai dari American stock loan. Begitupun dengan variasi nilai volatilitas. Apabila nilai volatilitas semakin meningkat maka nilai dari American stock loan juga meningkat.
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Stock loan is a contractual agreement involving two parties the lender, who provides the loan, and the borrower, who borrows the securities with collateral. The implementation mechanism of a stock loan is similar to an American call option. Therefore, stock loans can be evaluated using the Black-Scholes model, which follows the Geometric Brownian Motion. The model can be transformed into a non-dimensional form to simplify its structure. Subsequently, the model is solved using Laplace transforms. The solution obtained is in the form of a semi-analytic solution since its inversion involves numerical Laplace inversion using the Stehfest method. In the calculations, it is observed that the optimal exit price is increasing as the expiration time increases. This is directly proportional to the obtained value of the American stock loan. It is known that the higher the stock price and the longer the contract period, the higher the value of the American stock loan. The same applies to variations in the volatility parameter. If the volatility increases, the value of the American stock loan also increases.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Black-Scholes, Optimal exit price, Stock loan, Transformasi Laplace, Black-Scholes, Optimal exit price, Stock loan, Laplace transform
Subjects:	H Social Sciences > HG Finance H Social Sciences > HJ Public Finance
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Silda Sari Anggraini
Date Deposited:	28 Aug 2023 04:21
Last Modified:	28 Aug 2023 04:21
URI:	http://repository.its.ac.id/id/eprint/103108

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