CFA® Level I question of the day
18 October 2026 · Derivatives
Elena Vasquez prices options on the shares of a listed company that pays no dividends. A one-year forward on the shares trades at $105.00. One-year European options with a $100.00 strike are available, and the call is priced at $9.50. The risk-free rate is 4.00% per year. If put-call-forward parity holds, what is the price of the put with the same strike and expiry?
Show the answer and explanation
Answer: C. $4.69
Rearrange c + PV(X) = p + PV(F0) to p = c + PV(X) - PV(F0) = c - (F0 - X) / (1 + r)^T. Step 1: PV of the difference = (105.00 - 100.00) / 1.04 = $4.8077. Step 2: p = 9.50 - 4.8077 = $4.69. The forward is above the strike, so a long call with a short put at that strike has a positive value and the call must cost more than the put. The $4.50 answer skips the discounting (9.50 - 5.00). The $14.31 answer adds the discounted gap (9.50 + 4.81) and gets the sign of the relationship backwards.
- A. $4.50 - The gap between the forward price and the strike has not been discounted. Parity uses present values, so the $5.00 difference must be divided by 1.04 before it is netted against the call.
- B. $14.31 - The discounted difference was added to the call instead of subtracted. Because the forward price exceeds the strike, the call is worth more than the put, so the put must be lower.
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