Stochastic behavior in fertilizer prices

Abstract Purpose: To analyze the stochastic dynamics of fertilizer prices in Brazil by developing a synthetic NPK futures index weighted by Brazil’s fertilizer imports, and proposing a benchmark for over-the-counter (OTC) derivative development. Originality/value: This is the first study to implement stochastic convenience-yield modeling in Brazilian fertilizer markets, with a replicable methodology applicable to other agricultural commodity markets. Design/methodology/approach: Quantitative study using daily urea futures prices from the CME (Jun/2019 – Apr/2024) and monthly import data (Feb/2020 – Apr/2024). The Schwartz two-factor model is estimated using the Kalman filter to extract the stochastic convenience yield. A weighted NPK index (urea, MAP, potassium chloride) is constructed, and the filtered yield is applied to generate the synthetic futures index. Johansen cointegration tests, VECM, and minimum variance hedge ratios assess long-term relationships and hedging effectiveness. Findings: The synthetic index showed strong adherence to spot prices, with backwardation of -6.87%. Cointegration tests (trace: 61.55, p<0.01) confirmed a stable long-term equilibrium. Hedging effectiveness reached 95.8%, with hedge ratios ranging from 0.54 to 0.64 and significant deterioration beyond 5% volatility. Contribution/implications: Extends the commodity derivatives literature to an emerging-economy context, offering a practical benchmark for OTC derivatives and dynamic hedging strategies.