Many risk factors exist in the commodity markets, especially those related to price and quantity. Recently, the risk of counterparty default has been increasing. The purpose of this study is to develop a portfolio-hedging model to hedge both price and default risks using exchange traded commodity futures and option contracts. Two approaches are taken to determine the optimal hedge ratios (HR) using futures and options: an analytical approach that mathematically derives closed-form mean-variance (E-V) maximizing solutions, and an empirical approach that uses stochastic optimization and Monte Carlo simulation under mean-value-at-risk (E-VaR) framework. Based on the analytical approach, we proved that utility-maximizing solutions exists. The empirical approach suggests that naïve HR (HR of one) leads to a suboptimal result. The minimum-variance, E-V, and minimum VaR objective functions generated the same optimization results. Additionally, a copula is applied instead of a linear correlation, and resulted a higher put option HR.