Work on Problem $33)$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.

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