I've implemented the Derman-Kani tree with the Barle and Cakici modifications.I'm getting a problem when I increase the steps to move than about 50 for the data I've got.Basically around the 50th step, the edge nodes become so close together, they become equal. This then throws out the probabilities, and the tree doesn't return prices.To compensate, I test to see if the edge node is the same value as the node just inside it. If it is, I multiply it by a factor (1.00001 at the top, .99999 at the bottom, arbitrarily chosen) to prevent the values from being equal. This will of course widen the tree, but it does mean that I actually get numbers for probabilities.What I'm not so sure about is how valid this approach is. Does anyone have any thoughts on this?regards,dS