Optimal hedging and parameter uncertainty

Email: monoyios{at}maths.ox.ac.uk Received on 8 September 2006. Accepted on 15 March 2007. We explore the impact of drift parameter uncertainty in a basisrisk model, an incomplete market in which a claim on a nontradedasset is optimally hedged using a correlated traded stock. Usinganalytic expansions for indifference prices and hedging strategies,we develop an efficient procedure to generate terminal hedgingerror distributions when the hedger has erroneous estimatesof the drift parameters. These show that the effect of parameteruncertainty is occasionally benign, but often very destructive.In light of this, we develop a filtering approach in which thehedger updates her parameter estimates from observations ofthe asset prices, and we find an analytic solution to the hedger'scombined filtering and control problem in the case that thedrift of the traded asset is known with certainty.