Hey what is the replication strategy on the binomial tree when I have for example 10 step model and dividend is paid at step 3? I have a well-written price tree but I do not know what the replication strategy looks like because the price is not the same as in the case of using the martingale valuation. How does this one dividend impact replication strategy?
When the dividend is paid, the stock price on your tree should drop by the same amount. Ie if the dividend is 10 and the value of stock is 100 before the dividend at a node, you should change it to 90 and then continue building the tree from there. A cursory google brings quite a few results, eg this around slide 46 seems to explain it well