Valuation of commodity derivatives with an unobservable convenience yield

• Extend the literature: pricing commodity derivatives under incomplete information.
• Closed-form solutions for vanilla commodity derivatives under incomplete information.
• Commodity derivatives depend on initial values of the estimate and the estimation error.
• Empirical evidence: for futures prices our model seems to behave better than Schwartz׳s [11].
• Schwartz׳s model provide higher option prices than our model.

This paper extends the existing literature on commodity derivatives to account for an unobservable stochastic convenience yield. Investors operate in an economy with incomplete information. In contrast to other incomplete information models, analytical formulas for forward and futures prices, as well as for European options on forward and futures contracts are obtained. These formulas reveal the important role played by the initial values of the estimator of the convenience yield and of the estimation error respectively when valuing commodity derivatives. We estimate Schwartz׳s [11] model and the incomplete information model based on the discrete-time Kalman filtering method. For futures prices, the latter seems to perform better than the former. Moreover, Schwartz׳s model provides higher option prices than the incomplete information model. The most important differences are obtained for higher futures prices and for longer options maturities.