Work on Problem $3$

$3)$ 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 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.

There$$s another question that asks to use risk neutral probabilities but question $3$ asks for risk$-$free portfolios.

$4)$ Use risk neutral probabilities to calculate the value of a three$-$month European put with the strike price $50$ as in problem $3.$ Calculate the put value at each node of the tree.