The stock price of Heavy Metal $($HM$)$ changes only once a month: either it goes up by $20\%$ or it falls by $20\mathrm{.}1\%.$ Its price now is $$44.$ The interest rate is $0\mathrm{.}9\%$ per month.

What is the value of a one$-$month call option with an exercise price of $$44?$

What is the option delta?

The 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?

What is the value of a two$-$month call option with an exercise price of $$46?$

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