Answer:
$55.4930
Explanation:
Use the following formula to calculate the value of the call option
Value of call option = ( [tex]S_{0}[/tex] x N([tex]d_1[/tex]) ) - (K x [tex]e^{-rt}[/tex] x N([tex]d_2[/tex]))
where
[tex]S_{0}[/tex] = current spot price = $200
K = strike price = $180
r = risk-free interest rate
t is the time to expiry in years
N ([tex]d_1[/tex]) = NORMSDIST [ (ln(S0 / K) + (r + σ2/2) x T) / σ√T ] = NORMSDIST [ ln(200 / 180) + (0.21 + (0.2252/2) x 1 / 0.225 x √1 ] = 0.9350
N ([tex]d_2[/tex]) = NORMSDIST [d1 - σ√T ] = NORMSDIST [ 0.9350 - 0.225 x √1 ] = 0.9013
Placing values in the formula
Value of call option = ( $200 x 0.9350 ) - ($180 x [tex]e^{-(0.21)(1)}[/tex] x 0.9013)
Value of call option = $55.4930
