The price of a non-dividend paying stock is $55 per share.A 6-month,at the money call option is trading for $1.89.If the interest rate is 6.5%,what is the likely price of a European put at the same strike and expiration?
A) $0.05
B) $0.13
C) $0.56
D) $0.88

Question

Quizplus · Accepted Answer

To find the price of the European put option, we can use the Put-Call Parity formula for European options, which is: P + S = C + PV(X), where P is the price of the put, S is the current stock price, C is the price of the call, and PV(X) is the present value of the strike price (X), discounted back at the risk-free rate (r) over the life of the option (t). Since the option is at the money, the strike price is also $55. The formula rearranges to P = C + PV(X) - S.Given:- S = $55- C = $1.89- r = 6.5% or 0.065 (as a decimal)- t = 0.5 years (6 months)First, calculate PV(X):PV(X) = X / (1 + r)^t = $55 / (1 + 0.065)^0.5 ≈ $52.36Then, calculate P:P = $1.89 + $52.36 - $55 ≈ $0.13Therefore, the likely price of the European put option is $0.13.

The Price of a Non-Dividend Paying Stock Is $55 Per