Basis risk arises when hedging a financial derivative with an instrument different from its underlying asset. This risk can significantly impair hedging effectiveness and must therefore be properly managed. This article develops a discrete-time hedging framework for European-style derivatives that explicitly accounts for basis risk while incorporating key empirical properties of asset returns, including time-varying volatilities, leverage effects, and a flexible dependence structure between assets. Using a covariance-dependent pricing kernel, we derive semi-closed-form solutions for the optimal risk-minimizing hedge ratio. Empirical analyses using S&P 500 index data, its futures contracts, and the VIX demonstrate that our proposed strategy consistently outperforms conventional benchmarks across various maturities and moneyness levels, providing an effective approach to managing basis risk in derivative hedging.