Pricing Commodity Derivatives with Basis Risk and Partial Observations

We study the problem of pricing claims written on an over-the-counter energy contract. Because the underlying is illiquid, we work with an indifference pricing framework based on a liquid reference contract. Extending current convenience yield frameworks we propose a two-factor partially observed model for the benchmark asset. Moreover, we incorporate direct modeling of the unhedgeable basis. We then study the value function corresponding to utility pricing with exponential utility. After performing filtering this leads to an infinite-dimensional Hamilton-Jacobi-Bellman equation. We show that if the basis is totally independent, the indifference price of the claim is equal to its certainty equivalent. In the more interesting case where the basis depends on the unobserved factor we obtain a reduced-form expression for the price in terms of a conditional expectation. We show how to numerically compute this expectation using a Kalman or particle filter. Our basic model may be generalized to include nonlinear dynamics and further dependencies. Date: July 2006.