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FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

A non-dividend-paying stock is priced at 80. A European option has strike 75 and the present value of 1 paid at expiry is 0.95, so the discounted strike is 71.25. The model gives N(d1) = 0.80 and N(d2) = 0.70. What is the Black-Scholes-Merton price of the European put?

The put is worth 5.375. Using N(-d2) = 0.30 and N(-d1) = 0.20, put = 71.25 × 0.30 - 80 × 0.20 = 21.375 - 16. This is consistent with put-call parity, where the call of 14.125 minus the put equals 80 minus 71.25.

  1. A14.125
  2. B6.500
  3. C5.375Correct
  4. D-5.375

Explanation

Put = K e^(-rT) N(-d2) - S N(-d1) = 71.25(0.30) - 80(0.20) = 21.375 - 16 = 5.375. Check: the call is 80(0.8) - 71.25(0.7) = 14.125, and C - P = 8.75 = 80 - 71.25, so parity holds. Using the undiscounted strike gives 6.50, which is wrong.

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