Penentuan Harga Opsi Multiaset Tipe Eropa Menggunakan Jaringan Transformer Berbasis Backward Stochastic Differential Equation

Widianto, Aldi Eka Wahyu (2023) Penentuan Harga Opsi Multiaset Tipe Eropa Menggunakan Jaringan Transformer Berbasis Backward Stochastic Differential Equation. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Saham merupakan produk investasi kedua yang paling banyak diminati masyarakat Indonesia. Pemegang saham bisa mendapatkan keuntungan kapital apabila harga sahamnya mengalami kenaikan. Namun, karena harga saham bergerak secara stokastik, pemilik saham juga berisiko mengalami kerugian kapital apabila harga saham mengalami penurunan. Risiko ini dapat diatasi dengan membeli opsi. Harga opsi harus ditentukan secara tepat berdasarkan prinsip arbitrage-free. Metode penentuan harga opsi tradisional seperti metode binomial, beda hingga, dan Monte Carlo mengalami beberapa kendala dan tidak dapat digunakan untuk opsi yang terdiri dari banyak aset (multiaset). Kendala tersebut dapat diatasi dengan pendekatan deep neural network berbasis backward stochastic differential equation (BSDE). Tujuan utama dari tesis ini adalah untuk menentukan harga opsi multiaset tipe Eropa menggunakan jaringan Transformer berbasis BSDE. Penelitian ini diawali dengan formulasi BSDE dari persamaan harga opsi multiaset. Selanjutnya, arsitektur jaringan Transformer untuk mengaproksimasi solusi BSDE ditentukan. Setelah itu, jaringan Transformer dilatih menggunakan metode optimasi Adam. Pada penelitian ini jaringan Transformer diujikan untuk menentukan harga opsi basket put dan call tipe Eropa berdimensi 100. Hasilnya, jaringan Transformer dapat menentukan harga opsi secara akurat dengan persentase eror sebesar 0.8052% hingga 0.0371%. Selain itu, dibandingkan metode serupa yaitu Deep BSDE, jaringan Transformer terbukti lebih akurat, lebih cepat konvergen, dan membutuhkan waktu pelatihan yang lebih singkat.
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Stocks are the second most popular investment product in Indonesian society. Shareholders can get capital gains if the share price increases. However, since stock prices move stochastically, shareholders are also exposed to capital losses if the price declines. Shareholders can mitigate this risk by buying options. Option prices must be precisely determined based on the arbitrage-free principle. Traditional methods such as the binomial method, finite difference, and Monte Carlo encounter several limitations and cannot be used for pricing options consisting of multiple assets. These limitations can be addressed by using a deep neural network approach based on the backward stochastic differential equation (BSDE). The main objective of this thesis is to price a European-type multi-asset option using a BSDE-based Transformer network. This research begins with the BSDE formulation of the multiasset option price equation. Next, the Transformer network architecture to approximate the BSDE solution is determined. Subsequently, the Transformer network is trained using the Adam optimizer. In this study, the Transformer network was tested to determine the price of European-type basket put and call options with dimensions of 100. As a result, the Transformer network is able to accurately determine option prices with a percentage error of 0.8052% to 0.0371%. Additionally, compared to a similar method, namely Deep BSDE, the Transformer network is proven to be more accurate, converge faster, and require shorter training time.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	backward stochastic differential equation, deep neural network, jaringan Transformer, option pricing, penentuan harga opsi, Transformer network
Subjects:	Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions Q Science > QA Mathematics > QA76.87 Neural networks (Computer Science)
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis
Depositing User:	Aldi Eka Wahyu Widianto
Date Deposited:	15 Aug 2023 03:31
Last Modified:	15 Aug 2023 03:31
URI:	http://repository.its.ac.id/id/eprint/103219

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