The Trinomial Tree Method in Pricing European Gold Option with Volatility Forecasting Using the GARCH (1,1) Model

<table width="593" border="1" cellspacing="0" cellpadding="0"><tbody><tr><td valign="top" width="387"><p>This study enhances the pricing accuracy of European gold options by integrating GARCH (1,1)-based volatility forecast into the trinomial tree method. GARCH (1,1) captures key characteristics of financial return series, such as heteroscedasticity and volatility clustering, while the trinomial tree offers greater flexibility than traditional models by allowing three price movements at each node. This integration provides a more realistic and robust framework for option pricing under dynamic market conditions. Using gold price data from October 2017 to October 2024, the model forecast annualized volatilities of 16.59%, 17.33%, and 17.66% for one, two, and three months. For call options, prices increase with longer maturities, ranging from Rp194,048 to Rp207,385. Conversely, put options become more valuable when the strike price exceeds the market prices, reaching up to Rp107,778. The proposed model offers practical value for more accurate pricing and investment strategies.</p></td></tr></tbody></table>