Question

1. Show your work with the data below. (50 points) Calculate the call option value(Ve) of a call option with Black-Schokes Option Pricing Model Data: Vc Current value of the call option, P-current price of the underlying stock, $27 X-Exercise, or strike, price of the option, $25 KRF risk free interest rate, 6 % T-Time until the option expires (the option period) year, 6Months a-variance of the rate of return on the stock, 0.11 a standard deviation of the rate of the return on the stock, 0.3317 Ln(P/X)=national logarithm of P/X exponential function, 2.7183

please show work

Answer 1

Following is formula to calculate the value of call option under the Black-Scholes Model

Vc = P*N (d1) - N (d2) *X*e ^ (-r*t)               

Where

Vc = call value

P = current stock price = $27

N = cumulative standard normal probability distribution

t = days until expiration = 6 months = 0.5 years

Standard deviation, SD = σ = 0.3317

X = option strike price = $25

r = risk free interest rate = 6%

e = exponential function = 2.7183

Formula to calculate d1 and d2 are -

d1 = {ln (P/X) +(r+ σ^2 /2)* t}/σ *√t

= {ln(27/25) + (6%+0.11/2)*0.5}/0.3317 *√0.5

=0.5733

d2 = d1 – σ *√t

= 0.5733 – 0.3317*√0.5 = 0.3388

Now putting the value of d1 and d2 in above equation

Vc = $27*N (0.5733) - N (0.3388) *$25*2.7183 ^ (-6%*0.5)

= $4.0054

Call value (Vc) is $4.0054