A 2-month, $20 call option on ABC stock has an option premium of $0.40. The 2-month, $20 put option has an option premium of $1.60. The risk-free rate of interest is 5%. The options are European style. What is the price of ABC stock?
A) $15.23
B) $13.46
C) $18.64
D) $10.79
E) $17.41

Question

Quizplus · Accepted Answer

We can use put-call parity to solve for the stock price:

C + PV(X) = P + S

Where: 
C = call option premium = $0.40
PV(X) = present value of the strike price = X * e^(-rt) = 20 * e^(-0.05*2/12) = $19.49
P = put option premium = $1.60
S = stock price
t = time to expiration = 2 months / 12 months = 1/6
r = risk-free interest rate = 5%

Substituting the values:
0.40 + 19.49 = 1.60 + S
S = $18.29

Therefore, the price of ABC stock is $18.29. The closest choice is C, which is the correct answer.

A 2-Month, $20 Call Option on ABC Stock Has an Option