Plenty of material is written on how to hedge/arbitrage option price in one period binomial model, but I cannot find anything about hedging in multiple periods. If one to use multiple periods binomial model, how would one try to hedge? It seems like hedge ration always depends on the binary outcome of stock prices. Could somebody point me in the right direction?
Baxter and Rennie treat the multi-period model in chapter 2 and should be easy to follow.
The trick is to adjust the hedge ratio at every node. So you'll have holdings at time $t=1$ of $x_1$ and $y_1$ and different holdings on $x_2$ and $y_2$ and so on for all the steps. The holdings, except for the first one, depend on the history of up or down moves.