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The current price of ABC stock is $200. The standard deviation is 22.5 percent a year and the interest rate is 21 percent a year. A one-year call option has an exercise price of $180.00. Use Black-Scholes to value a call option on ABC.

Sagot :

Hyderali230idn

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

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