Consider a European and an American call option written on an underlying security with initial price

$S_0=100,$ paying a dividend after $9$ months computed with a yield equal to $2\%,$ strike price $K=$

$105,$ maturity $T=1$ year. Compute the option prices with the Cox$-$Ross$-$Rubinstein model with $n=$

$4$ time steps with volatility $=0\mathrm{.}2$ and continuously compounded rate of return $r=0\mathrm{.}03$ on a

yearly basis.