Assume the underlying stock follows the following binomial tree with the true probability measure P as labeled. Price a digital contract that pays off $100 in 6 month (at time 2?t ) if the stock price at time 2?t ends higher than where it started at time zero. Please calculate hedge ratio at each relevant nodes on the tree. Suppose risk-free rate is r=5% and time interval is one quarter, that is, ??t =0.25.