A stock price is currently $50$ and after $6-$months it can be either $60$ or $42.$ The risk$-$free

rate is $12\%($continuous compounding$).$ The no$-$arbitrage price of a $6-$month european

call option written on this stock with strike $50$ is

$($a$)2\mathrm{.}89($b$)3\mathrm{.}61($c$)4\mathrm{.}64($d$)5\mathrm{.}80($e$)6\mathrm{.}96$

is the answer $-$At the end of six months the value of the option will be either $C_u=$$$12($if the stock price is $$60)$ or $C_d=$$$0$

$($if the stock price $C_d=$$$42).$ Moreover, $u=\frac{60}{50}=1\mathrm{.}2,d=\frac{42}{50}=\mathrm{.}84$ and $R=e^{12\%\frac{6}{12}}=1\mathrm{.}02$ so that the

risk$-$neutral probability of $"$up$"$ is $q=\frac{R-d}{u-d}=0\mathrm{.}616.$ The value of the option is therefore

$C=\frac{1}{R}[q{C}_u+(1-q)C_d]=$$$6\mathrm{.}96$

or is the answer $5\mathrm{.}8????$