In this article we derive tractable analytic solutions for futures and options prices for a linear-quadratic jump-diffusion model with seasonal adjustments in stochastic volatility and convenience yield. We then calibrate our model to data from the fish pool futures market, using the extended Kalman filter and a quasi-maximum likelihood estimator and alternatively using an implied-state quasi-maximum likelihood estimator. We find no statistical evidence of jumps. However, we do find evidence for positive correlation between salmon spot prices and volatility, seasonality in volatility and convenience yield. In addition we observe a positive relationship between seasonal risk premium and uncertainty of EU salmon demand. We further show that our model produces option prices that are conform with the observation of implied volatility smiles and skews. Our work connects to a number of results that have recently appeared in the Operations Research literature.

在本文中，我们获得了具有随机波动性和便利收益率的季节性调整的线性二次跳跃扩散模型的期货和期权价格的可解析分析解决方案。然后，我们使用扩展的卡尔曼滤波器和准最大似然估计器，或者使用隐含状态准最大似然估计器，将模型校准为来自鱼池期货市场的数据。我们找不到跳跃的统计证据。但是，我们确实发现了鲑鱼现货价格与波动性，波动性的季节性和便利性产量之间呈正相关的证据。此外，我们发现季节性风险溢价与欧盟鲑鱼需求的不确定性之间存在正相关关系。我们进一步证明，我们的模型产生的期权价格与隐含波动率微笑和偏斜的观察结果一致。