Consider a two period, two scenario world where a stock price is $$45,$ the risk$-$free rate is

$5\%$ and the stock can either go up $20\%$ or down $20\%$ over one year $($i$.$e$.1\mathrm{.}20$ or $\mathrm{.}80).$ A call

option expiring at the end of the second period has an exercise price of $$40.$

$($a$)$ Use the two period binomial model to calculate the value of the call at $T=0.$

$($b$)S_{}=$

$($c$)S_{ud}=$

$($d$)S_u=$

$($e$)S_d=$

$($f$)S_{dd}=$

$($g$)C_{}=$

$($h$)C_{ud}=$

$($i$)C_u=$

$($j$)C_d=$

$($k$)C_{dd}=$

$(1)$ Calculate $h$ at $T=0.$

$($m$)$Calculate $h_u$ at $T=1$

$($n$)$ Calculate $h_d$ at $T=1$