Stochastic price process models of rolling gold traded in Indonesia market

Abstract

Modeling commodity price process represented by a stochastic differential equation is essential for developing the risk managent tools, e.g., options, besides for forecasting future prices. However, gold has spesific features compared to other commodities such as agricultural and energy commodies, even compared to other metals. Gold is the most popular commodity used as an investment. Hence, gold is often used to hedge the risks against economic, political, social or currency-based crisis. We model the rolling gold spot prices traded in Indonesia market as commonly applied to model the commodity price, that is as the the sum of the deterministic and stochastic components. Our investigation shows that the gold price process does not exhibit seasonality but presents trend influenced by inflation. That feature is captured as the deterministic component model. To describe the stochastic component, we investigate performances of three models: Geometric Brownian Motion, mean-reversion diffusion and potential diffusion models. Performances of those three models are measured by comparing the distributional characteristics obtained from the original data and from those models to find the most suitable model for rolling gold prices. Then, based on the most suitable model, we forecast future spot rolling gold prices and apply some statistical tests to investigate performances of the model.