Question

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.

Answer 1

$55.4930

Step-by-step explanation:

Use the following formula to calculate the value of the call option

Value of call option = (
`S_(0)` x N(
`d_1`) ) - (K x
`e^(-rt)` x N(
`d_2`))

where

`S_(0)` = current spot price = $200

K = strike price = $180

r = risk-free interest rate

t is the time to expiry in years

N (
`d_1`) = 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 (
`d_2`) = 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
`e^(-(0.21)(1))` x 0.9013)

Value of call option = $55.4930