The stock price of Boggle Corporation changes only once a month: either it goes up by $16\mathrm{.}0\%$ or it falls by $12\mathrm{.}0\%.$ Its current share price is $$55\mathrm{.}00.$ The interest rate is approximately $1\mathrm{.}3\%$ per month.

Required:

$($a$)$ Using the risk$-$neutral method, calculate the value of a one$-$month call option with an exercise price of $$55\mathrm{.}00.$

$(6$ marks$)$

$($b$)$ What is the option delta?

$(4$ marks$)$

$($c$)$ Show how the payoffs of this call option can be replicated by buying Boggle$$s stock and borrowing.

$(6$ marks$)$

$($d$)$ Using the binomial method, what is the value of the two$-$month call option with an exercise price of $$55\mathrm{.}00?$

$(6$ marks$)$

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

$(3$ marks$)$

$($f$)$ Briefly explain the factors that drive the price of a call option.

$(5$ marks$)$