$3)$ A stock price is $$50$ now. In $1$ month it can go $5\%$ up or down. In the second month it can go $5\%$ up or down. And in the third month it can go $5\%$ up or down. Construct a binomial tree for this stock. The annual interest rate is $10\%$ with continuous compounding. Use risk$-$free portfolios $(not$ risk neutral$)$ to calculate the value of a three$-$ month European put with the strike price $50.$ Calculate the Delta at each node of the tree. Calculate the put value at each node of the tree.