Dunbar - I think this was discussed earlier in the thread, but the basic idea is this: local vols is a particular choice of model. Its goodness or badness is determined by how well it predicts things like moves in the implied volatilities as the underlying asset moves around.Those predictions feed back into the Delta calculations, which determine what hedges you'll put on.So imagine two cases: one, you hedge a barrier using the regular Black-Scholes Deltas; the other, you calibrate a local vol model and use that to calculate the Deltas you hedge with. Which one results in a better hedge? You can attempt to answer this by using historical data and doing trading simulations off it.In many markets (G7 fx being one), if you do that you end up with the local vol hedge being a *worse* hedge than regular Black-Scholes, in the sense that the distribution of PNL over the life of the option has a larger standard deviation.Pricing and hedging are two sides to the same coin: the price of a derivative is the expected dynamic hedging costs over its life. If your model doesn't get the hedges correct, it won't get the price correct either.Local vols is an attractive model because it's easy to implement. But don't let that trick you into thinking it's a good model. Maybe it is for your market, or maybe it isn't - you have to test it by doing things like trading simulations and looking at parameter stability over time. There are lots of models which all match the current implied vols but predict quite different prices for barriers.

McHiggins:In FI markets, and for European options, the difference in hedges between local vol model and the Black Scholes model (with the correct implied vol) seems to have the right magnitude but the wrong sign.

HiThanks for the answers. But how is delta actually calculated from this type of tree? Isn't the hedge quality heavily dependent on the theoretical vanilla prices used in re-calibration?Best regards - Dunbar