Electronic Theses and Dissertation

Dalam upaya meminimalkan risiko investasi, instrumen derivatif seperti opsi telah dikembangkan. Opsi memberikan hak, tetapi bukan kewajiban, kepada pemegangnya untuk membeli atau menjual suatu aset pada harga tertentu (strike price) dalam jangka waktu yang telah ditentukan. Namun, tantangan utama yang dihadapi investor adalah kurangnya pemahaman dan strategi yang tepat dalam menentukan harga opsi. Salah satu permasalahan signifikan adalah perhitungan volatilitas menggunakan standar deviasi yang umum digunakan dalam banyak penelitian, padahal volatilitas pasar sering kali bersifat heteroskedastis dan menunjukkan fenomena volatility clustering. Penelitian ini menggunakan model GARCH(1,1) untuk meramalkan volatilitas harga emas, yang mampu menangkap sifat heteroskedastisitas dan fenomena volatility clustering. Selain itu, penelitian ini juga menjawab keterbatasan penelitian sebelumnya yang lebih banyak fokus pada opsi saham dibandingkan kontrak opsi emas, padahal minat terhadap emas sebagai instrumen investasi terus meningkat. Dalam penentuan harga opsi akan digunakan metode trinomial yang merupakan pengembangan dari metode binomial. Metode trinomial mengasumsikan harga aset dapat bernilai tetap bukan hanya bernilai naik atau turun, sehingga lebih fleksibel dalam mencerminkan kondisi pasar aktual. Probabilitas pergerakan harga tetap dalam metode trinomial dihitung berdasarkan data historis harga emas periode Oktober 2017 hingga Oktober 2024, sehingga parameter yang digunakan lebih relevan dengan kondisi pasar sebenarnya. Analisis dilakukan untuk berbagai kasus, termasuk perbandingan strike price yang lebih besar, lebih kecil, atau sama dengan harga aset awal, serta waktu jatuh tempo (time to maturity) selama 1, 2, dan 3 bulan. Hasil penelitian menunjukkan bahwa harga opsi beli (call option) cenderung menurun dengan meningkatnya strike price, sementara harga opsi jual (put option) cenderung meningkat. Selain itu, harga opsi beli (call option) maupun opsi jual (put option) cenderung meningkat seiring bertambahnya waktu jatuh tempo.
Kata Kunci: Opsi Eropa, Peramalan Volatilitas, Model GARCH(1,1), Metode Pohon Trinomial.

In order to mitigate investment risk, derivative instruments such as options have been developed. Options offer the holder with the right, but not the obligation, to buy or sell an asset at a predetermined price (strike price) within a specific time period. However, a significant challenge faced by investors lies in the lack of understanding and proper strategies for calculating option prices. One major issue is the calculation of volatility using standard deviation, which is commonly applied in many studies, despite the fact that market volatility is often heteroskedastic and exhibits the phenomenon of volatility clustering. This study employs the GARCH(1,1) model to forecast gold price volatility, as it is capable of capturing heteroskedasticity and volatility clustering. Furthermore, this research addresses the limitations of previous studies that predominantly focus on stock options, overlooking gold option contracts, even though the growing interest in gold as an investment instrument makes the development of accurate pricing methods for gold options increasingly relevant. The trinomial method, an extension of the binomial method, is used in this study to examine option prices. The trinomial method assumes that asset prices can remain constant, rise, or fall, making it more flexible in reflecting actual market conditions. The probability of constant price movement in the trinomial method is calculated based on historical gold price data from October 2017 to October 2024, ensuring that the derived parameters align more closely with actual market conditions. The analysis covers various scenarios, including comparisons of strike prices that are greater than, less than, or equal to the initial asset price, as well as time to maturity (time to maturity) over 1, 2, and 3 months. The results reveal that the price of call options tends to decrease as the strike price increases, while the price of put options exhibits the opposite trend. Furthermore, both call and put option prices tend to rise as the time to maturity increases. Keywords: European Option, Volatility Forecasting, GARCH(1,1) Model, Trinomial Tree Method.