Consider $S=105,$ a continuously compounded interest rate $r=4\%,$ continuous dividend yield $=2\%,$ and volatility $=0\mathrm{.}3.T=1.$

a$)$ Based on the parameters above, construct a binomial tree with $n=3$ periods.

b$)$ Find the price of a $115-$strike European call option using the binomial tree on a$).$ For the initial node give the composition of the

replicating portfolio $($that is the values of $$ and $B).$

c$)$ Find the price of a $115-$strike European put option using the binomial tree on a$).$

d$)$ Verify that your answers to part b$)$ and c$)$ satisfy the put$-$call parity relationship.

e$)$ Find the price of a $115-$strike American put option using the binomial tree on a$).$