FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model
A European call on a non-dividend-paying stock is priced at 9.50. The stock trades at 100, and the call and a European put on the same stock both have strike 100 and maturity 1 year. The continuously compounded risk-free rate is 4% (e^{-0.04} = 0.960789). Using put-call parity, what is the put price?
The put price is 5.58. Put-call parity gives put = call + present value of strike - stock price, so 9.50 + 96.08 - 100 = 5.58. Ignoring discounting would give 9.50, and flipping the signs would give 13.42.
- A5.58Correct
- B9.50
- C13.42
- D3.92
Explanation
Parity: p = c + K e^{-rT} - S0 = 9.50 + 96.08 - 100 = 5.58. Setting p = c ignores discounting (9.50). Reversing the signs gives 13.42. Leaving out the call price gives 3.92.
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