I am trying to value an american call option with a lookback feature. So the holder can choose to exercise either based on a fixed strike (K) or a floating strike equal to 10-day moving average (MA). I tried to build a tree model but results look weird and I couldn't figure out where the problem is. What I did is to construct trees for stock price (S) and 10-day moving average price, and then using backward induction to compare the exercise value vs. the continuation value at each node (ie. max(max(0, S-K, MA-K), continuation value)). It sounds pretty intuitive but I keep getting really low delta (like 0.6) for deep in the money options. Anyone came cross the same instruments and happen to have a good idea how to model it?