Optimal hedging and parameter uncertainty

We explore the impact of drift parameter uncertainty in a basis risk model, an incomplete market in which a claim on a nontraded asset is optimally hedged using a correlated traded stock. Using analytic expansions for indifference prices and hedging strategies, we develop an efficient procedure to generate terminal hedging error distributions when the hedger has erroneous estimates of the drift parameters. These show that the effect of parameter uncertainty is occasionally benign, but often very destructive. In light of this, we develop a filtering approach in which the hedger updates her parameter estimates from observations of the asset prices, and we find an analytic solution to the hedger's combined filtering and control problem in the case that the drift of the traded asset is known with certainty.