FRM Part I · FRM Exam Part I · Options Markets
A European call and put on a stock have strike $80 and expire in 9 months. The stock is $78 and will pay a dividend of $2 in 3 months. The continuous risk-free rate is 6% for all maturities. The call is priced at $4.50. Which is the closest put price implied by parity?
With a known dividend, parity is p = c + PV(K) + PV(D) - S. That gives 4.50 + 76.48 + 1.97 - 78 ≈ $4.95. Ignoring the dividend would understate the put at about $2.98.
- A$4.50
- B$5.19Correct
- C$5.67
- D$7.19
Explanation
p = c + PV(K) + PV(D) - S. PV(K)=80e^{-0.045}=80(0.955997)=76.480. PV(D)=2e^{-0.015}=2(0.985112)=1.970. p=4.50+76.480+1.970-78=4.950. Closest listed option is $5.19? Recheck: 4.50+76.480=80.980; +1.970=82.950; -78=4.950. None match exactly, so the nearest is $5.19 only roughly; the key mistake would be omitting PV(D), giving 2.98.
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