Penentuan Solusi Persamaan Opsi Barrier Melalui Bentuk Backward Stochastic Differential Equations

Teguh, Prima (2024) Penentuan Solusi Persamaan Opsi Barrier Melalui Bentuk Backward Stochastic Differential Equations. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Opsi barrier merupakan suatu instrumen keuangan yang memberikan hak kepada pemegangnya untuk membeli atau menjual aset acuan hanya jika harga aset tersebut mencapai atau melewati tingkat barrier tertentu. Penentuan harga opsi barrier adalah masalah yang kompleks karena melibatkan kondisi terminal yang tergantung pada pergerakan harga aset acuan. Salah satu pendekatan yang digunakan untuk mengatasi masalah ini adalah menggunakan Backward Stochastic Differential Equations (BSDEs). BSDEs merupakan Persamaan Differensial Stokastik dengan kondisi batas yang dimulai dari waktu akhir ke waktu awal. Tujuan penelitian tesis ini adalah menentukan Persamaan Black-Scholes opsi barrier jenis down-and-out tipe call dengan menggunakan BSDEs. Proses tersebut dilakukan dengan beberapa cara yaitu konstruksi model portofolio yang berbentuk BSDEs, uji eksistensi model portofolio BSDEs, pembentukan Model Black-Scholes dengan Teorema Feynman-Kac, dan solusi analitik dengan persamaan difusi. Sebagai aplikasi, memerlukan simulasi dengan tujuan untuk mengetahui pengaruh harga opsi barrier berdasarkan beberapa asumsi parameter yaitu harga saham, strike price, harga barrier, volatilitas, suku bunga bebas risiko, suku bunga dividen, dan waktu. Hasil dari simulasi tersebut adalah semakin besar volatilitas dan suku bunga bebas risiko, harga opsi akan semakin besar. Semakin besar strike price dan harga barrier, juga semakin besar harga opsi namun payoff barrier akan semakin besar. Akibatnya harga opsi bisa tembus atau melewati harga barrier. Penambahan dividen juga mempengaruhi pergerakan harga opsi dan payoff barrier. Jika suku bunga dividen lebih besar dari suku bunga bebas risiko, maka kemungkinan harga opsi akan berada di bawah harga barrier
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A barrier option is a financial instrument that entitles to the holder to buy or sell the underlying asset only if the price of the asset reaches or passes a certain barrier level. Pricing a barrier option is a complex problem because it involves terminal conditions that depend on the price movement of the underlying asset. One approach used to address this problem is to use Backward Stochastic Differential Equations (BSDEs). BSDEs are Stochastic Differential Equations with boundary conditions that start from the end time to the beginning time. The purpose of this thesis research is to determine the Black-Scholes Equation of the down-and-out call type barrier option using BSDEs. The process is carried out in several ways, namely the construction of a portfolio model in the form of BSDEs, the existence test of the BSDEs portfolio model, the formation of the Black-Scholes Model with the Feynman-Kac Theorem, and the analytical solution with the diffusion equation. As an application, it requires simulation with the aim of knowing the effect of barrier option prices based on several parameter assumptions, namely stock prices, strike prices, barrier prices, volatility, risk-free interest rates, dividend interest rates, and time. The result of the simulation is that the greater the volatility and risk-free interest rate, the greater the option price. The larger the strike price and barrier price, the larger the option price but the larger the payoff barrier. As a result, the option price can break through or pass the barrier price. The addition of dividends also affects the movement of the option price and payoff barrier. If the dividend rate is greater than the risk-free rate, it is likely that the option price will be below the barrier price.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Opsi Barrier, Backward Stochastic Differential Equations (BSDEs), Harga Opsi, Kondisi Terminal, Teorema Feynman-Kac
Subjects:	Q Science > QA Mathematics > QA274.2 Stochastic analysis Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis
Depositing User:	M.Prima Teguh Aliffrianto
Date Deposited:	09 Aug 2024 02:13
Last Modified:	11 Sep 2024 01:24
URI:	http://repository.its.ac.id/id/eprint/113693

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