<![CDATA[Cocoa (Theobroma cacao) is one of Indonesia's most strategically significant agricultural export commodities, yet its price dynamics are characterized by extreme volatility that imposes substantial financial risk on stakeholders across the supply chain. Standard statistical models that assume Gaussian or light-tailed distributions systematically underestimate the probability and severity of extreme price movements, leading to inadequate risk management practices. This paper proposes a rigorous tail risk estimation framework for Indonesian cocoa commodity prices using Extreme Value Theory (EVT), specifically the Generalized Pareto Distribution (GPD) fitted via the Peaks-Over-Threshold (POT) method. The optimal threshold is selected using the Mean Excess Plot (MEP) and the Hill estimator, while GPD parameters are estimated through Maximum Likelihood Estimation (MLE). The framework quantifies tail risk through Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) at multiple confidence levels (90%, 95%, 99%, 99.5%, and 99.9%) and constructs return-level plots for risk horizon analysis. Comparative analysis against the Normal distribution and Student-t distribution confirms that the GPD-POT approach provides a significantly superior fit to the empirical tail of cocoa log-returns, as evidenced by the Kolmogorov-Smirnov test, Anderson-Darling test, and Q-Q diagnostic plots. The shape parameter estimate ξ = 0.2758 confirms the presence of heavy tails (Fréchet domain), indicating a higher frequency of extreme price events than predicted by thin-tailed models. The estimated 99% VaR of 6.301% and CVaR of 9.142% provide actionable benchmarks for hedging strategies, insurance premium calculations, and commodity trading risk limits. This study contributes a statistically sound, threshold-based EVT methodology applicable to agricultural commodity risk management in emerging markets.]]>
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