We investigate calibrating financial models using a rigorous Bayesian framework. Non-parametric approaches in particular are studied and the local volatility model is used throughout as an example. By incorporating potential calibration error into our method we design optimal hedges that minimiseexpected loss statisticsbased on different Bayesianlossfunctions decided by an investor’s preferences. Comparisons made with the standard hedge strategies show the Bayesian hedges to outperform traditional methods. 1