The share price of Heavy Metal $($HM$)$ changes only once a month:

Either it goes up by $26\%$ or it falls by $19\mathrm{.}3\%.$ Its price now is $$42\mathrm{.}7.$ The interest rate is $0\mathrm{.}5\%$ per month.

a$.$ What is the value of a one$-$month call option with an exercise price of $$42\mathrm{.}7?$

b$.$ What is the option delta?

c$.$ he payoffs of the call option can be replicated by buying shares of stock and borrowing. What amount should be invested in stock and what amount must be borrowed?

d$.$ What is the value of a two$-$month call option with an exercise price of $$42?$

e$.$ What is the option delta of the two$-$month call over the first one$-$month period?