FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model
A European call on a non-dividend-paying stock has a strike of 48, six months to expiry and a market price of 4.20. The stock trades at 50 and the continuously compounded risk-free rate is 4% per year. Using put-call parity, which value is closest to the price of a European put with the same strike and expiry?
The put is worth about 1.25. Put-call parity gives P = C - S + K e^(-rT), which is 4.20 - 50 + 48 times e^(-0.02), or 47.05. The strike must be discounted at the risk-free rate; leaving it undiscounted would give 2.20 instead.
- A1.25Correct
- B2.20
- C3.17
- D7.15
Explanation
P = C - S + K e^(-rT) = 4.20 - 50 + 48 e^(-0.02) = 4.20 - 50 + 47.05 = 1.25. Ignoring discounting of the strike gives 2.20. Compounding the strike forward instead of discounting it gives about 3.17. Reversing the sign on S gives 7.15.
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