FRM Part I · FRM Exam Part I · Properties of Options
A non-dividend-paying stock trades at 52. A European call with strike 50 and one year to expiry is priced at 6.00. The continuously compounded risk-free rate is 4% per year. Assuming put-call parity holds, what is the price of the European put with the same strike and expiry?
The put is worth about 2.04. Put-call parity states p = c + PV(K) - S0, so 6 + 48.04 - 52 = 2.04. The strike must be discounted at the risk-free rate; leaving it undiscounted gives 4.00, which is wrong.
- A2.04Correct
- B4.00
- C9.96
- D4.08
Explanation
Parity gives p = c + K e^(-rT) - S0 = 6 + 50 e^(-0.04) - 52 = 6 + 48.04 - 52 = 2.04. Ignoring discounting gives 4.00. Discounting the stock price instead of the strike gives 4.08. Reversing the signs on the call and the stock gives 9.96.
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