Crop yields and harvest prices are often considered to be negatively correlated, thus acting as a natural risk management hedge through stabilizing revenues. Storage theory gives reason to believe that the correlation is an increasing function of stocks carried over from previous years. Stock-conditioned second moments have implications for price movements during shortages and for hedging needs, while spatially varying yield-price correlation structures have implications for who benefits from commodity support policies. In this paper, we propose to use semi-parametric quantile regression (SQR) with penalized B-splines to estimate a stock-conditioned joint distribution of yield and price. The proposed method, validated through a comprehensive simulation study, enables sampling from the true joint distribution using SQR. Then it is applied to approximate stock-conditioned correlation and revenue insurance premium for both corn and soybeans in the United States. For both crops, Cornbelt core regions have more negative correlations than do peripheral regions. We find strong evidence that correlation becomes less negative as stocks increase. We also show that conditioning on stocks is important when calculating actuarially fair revenue insurance premiums. In particular, revenue insurance premiums in the Cornbelt core will be biased upward if the model for calculating premiums does not allow correlation to vary with stocks available. The stock-dependent correlation can be viewed as a form of tail dependence that, if unacknowledged, leads to mispricing of revenue insurance products.

翻译：作物产量与收获价格通常被认为呈负相关关系，从而通过稳定收入发挥自然风险管理对冲作用。库存理论表明，这种相关性是往年结转库存的递增函数。基于库存条件的二阶矩对短缺时期的价格波动及对冲需求具有重要影响，而空间异质性产量-价格相关结构则关系到商品支持政策的受益群体。本文提出采用含惩罚B样条的半参数分位数回归（SQR）方法，估计基于库存条件的产量与价格联合分布。通过全面模拟研究验证，该方法能够利用SQR从真实联合分布中抽样。进而应用于近似估算美国玉米和大豆的库存条件相关性及收入保险保费。研究表明，两种作物的玉米带核心区域呈现比边缘区域更强的负相关性。我们获得有力证据显示，随着库存增加，负相关性会减弱。同时证明，在计算精算公平收入保险保费时，考虑库存条件至关重要。特别地，若保费计算模型不允许相关性随可用库存变化，玉米带核心区域的收入保险保费将被高估。这种库存依赖的相关性可视为一种尾部依赖形式，若未被识别将导致收入保险产品错误定价。