Now consider pricing call and put options on a $2-$step binomial tree. Each step on the binomial tree is one year. The current stock price is $$50,u=1\mathrm{.}20,d=0\mathrm{.}80,$ and the continuously compounded interest rate is $5\%.$ Answer questions $19$ to $24$ using this information.

What is the replicating portfolio at the beginning node of the binomial tree of a $2-$year American call option with a strike price of $$52?$

A$.$ Buy $0\mathrm{.}5975$ shares and borrow $$18\mathrm{.}74.$

B$.$ Buy $0\mathrm{.}5975$ shares and borrow $$22\mathrm{.}74.$

C$.$ Buy $0\mathrm{.}6833$ shares and borrow $$26\mathrm{.}32.$

D$.$ Buy $0\mathrm{.}6833$ shares and borrow $$22\mathrm{.}32.$

E$.$ Buy $0\mathrm{.}7112$ shares and borrow $$24\mathrm{.}18.$