Question

Use the following information to answer the next two questions.

MNO stock currently trades for $75. Call options on the stock mature in six months and have a strike price of $75. The expected standard deviation of the stock is 20% and the annual risk-free rate is 6%.

1) What should be the call premium according to the Black-Scholes model?

2) Use the Black-Scholes model to find the premium for a put option on MNO that expires in six months and has an exercise price of $75. Round intermediate steps to four decimals.

Thank you

Answer 1

1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		75
t = time to expiry =		0.5
K = Strike price =		75
r = Risk free rate =		6.0%
q = Dividend Yield =		0%
σ = Std dev =		20%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(75/75)+(0.06-0+0.2^2/2)*0.5)/(0.2*0.5^(1/2))
d1 = 0.282843
d2 = d1-σ*t^(1/2)
d2 =0.282843-0.2*0.5^(1/2)
d2 = 0.141422
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.611351
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.556232
Value of call= 75*0.611351-0.556232*75*e^(-0.06*0.5)
Value of call= 5.37

2

As per Black Scholes Model
Value of put option = N(-d2)*K*e^(-r*t)-(S)*N(-d1)
Where
S = Current price =		75
t = time to expiry =		0.5
K = Strike price =		75
r = Risk free rate =		6.0%
q = Dividend Yield =		0%
σ = Std dev =		20%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(75/75)+(0.06-0+0.2^2/2)*0.5)/(0.2*0.5^(1/2))
d1 = 0.282843
d2 = d1-σ*t^(1/2)
d2 =0.282843-0.2*0.5^(1/2)
d2 = 0.141422
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.388649
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.443768
Value of put= 0.443768*75*e^(-0.06*0.5)-75*0.388649
Value of put= 3.15