CFA Level IDerivativesMedium
A stock currently trades at $50. A European call option with a strike price of $52 and six months to expiration is priced at $4.00. The risk-free rate is 5% annually. Using put-call parity, what should be the price of a European put option with the same strike and expiration?
- A$1.25
- B$4.75
- C$2.00
- D$6.00
Show answer & explanationAnswer & explanation
Correct answer: B. $4.75
Put-call parity states p = c - S0 + PV(X). PV(X) = 52/(1.05)^0.5 = 52/1.0247 = 50.75. Therefore, p = 4 - 50 + 50.75 = $4.75.
Why the other options are wrong
- A. This results from a discounting or sign error in the parity formula.
- C. This fails to discount the strike price back to present value.
- D. This incorrectly adds the strike price rather than using its present value.
Put-Call Parity
A no-arbitrage relationship linking the prices of European calls and puts with the same strike and expiration: c + PV(X) = p + S0.
- p = c - S0 + PV(X)
- c = p + S0 - PV(X)
- Assumes European-style options and no dividends
Memory trick: Fiduciary call equals protective put — balance the equation to isolate the missing price.