Question

suppose the standard deviation of a stocks return is 25% per year and the riskless return is 10% APR.Answer the below questions using the Black -Scholas OPM. A. What is a 6 month call option on this stock worth if the strick price is $90 and the stock price is(Po)is currently at$104? B.what is the exercise value and the time premiumof this optrion? C.Everything else being equal,what is the value of a 6 month put option on the common stock?Use call- put parity.

Answer 1

a

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*r^(-r*t)
Where
S = Current price =		104
t = time to expiry =		0.5
K = Strike price =		90
r = Risk free rate =		10.0%
q = Dividend Yield =		0%
σ = Std dev =		25%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(104/90)+(0.1-0+0.25^2/2)*0.5)/(0.25*0.5^(1/2))
d1 = 1.189106
d2 = d1-σ*t^(1/2)
d2 =1.189106-0.25*0.5^(1/2)
d2 = 1.012329
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.882801
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.84431
Value of call= 104*0.882801-0.84431*90*e^(-0.1*0.5)
Value of call= 19.53

b
Exercise value = Current price-strike = 104-90=14

Time value = value of call-exercise value = 19.53-14 = 5.53

C

As per put call parity

Call price + PV of exercise price = Spot price + Put price

19.53+90*e^(-0.1*0.5)=104+Put value

Put value = 1.14