Question

# Use the Black-Scholes formula to find the value of a call option based on the following...

Use the Black-Scholes formula to find the value of a call option based on the following inputs. (Round your final answer to 2 decimal places. Do not round intermediate calculations.)

 Stock price \$ 12.00 Exercise price \$ 5.00 Interest rate 5.00 % Dividend yield 4.00 % Time to expiration 0.4167 Standard deviation of stock’s returns 31.00 %

Call value            \$

Stock Price = S = \$ 12, Exercise Price = X = \$ 5, Initerest Rate = r = 5 %, Dividend yield = q = 4 %,Time to Expiration = t = 0.4167 and Standard Deviation of the Stock = = 31 %

The Black-Scholes Formula is as given below in the image:

d1 = [ln(12/5) + 0.4167 x {0.05 - 0.04 + (0.31)^(2)/2} ]/ 0.31 x (0.4167)^(0.5) = 4.49577

d2 = 4.49577 - 0.31 x (0.4167)^(0.5) = 4.29566

Call Option Value = C = [N(4.49577) x 12] / EXP(0.04 x 0.4167) - [N(4.29566) x 5] / EXP(0.05 x 0.4167) = [0.999997 x 12] / EXP(0.04 x 0,4167) - [0.999991 x 5[ / EXP(0.05 x 0,4167) = \$ 6.905 or \$ 6.91 approximately.

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