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

A European call on a stock has a value of 8.00. The stock price is 100, the strike is 100, the risk-free rate is 5% continuously compounded, the stock pays a continuous dividend yield of 3%, and the time to expiry is one year. What is the value of the European put with the same strike and expiry, using put-call parity?

The put is worth about 6.08. Put-call parity with a dividend yield states that the call plus the present value of the strike equals the put plus the stock price discounted at the yield. This gives 8 plus 95.12 minus 97.04, which is 6.08.

  1. A0.08
  2. B3.12
  3. C6.08Correct
  4. D10.96

Explanation

Parity with a yield is c + K*e^(-rT) = p + S0*e^(-qT). Then p = 8 + 100*0.951229 - 100*0.970446 = 8 + 95.123 - 97.045 = 6.08. Ignoring the yield gives 3.12. Using e^(+qT) gives 0.08. Ignoring the discounting of the strike gives 10.96.

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