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FRM Part I · FRM Exam Part I · Properties of Options

A stock priced at 40 pays a continuous dividend yield of 3% per year. The continuously compounded risk-free rate is 5%. For European options with strike 42 and one year to expiry, what is the difference c - p implied by put-call parity?

The call minus the put is about -1.13. With a dividend yield, parity says c - p equals the spot price discounted at the yield minus the strike discounted at the risk-free rate: 38.82 minus 39.95, which is about -1.13.

  1. A-1.13Correct
  2. B0.05
  3. C-3.18
  4. D1.13

Explanation

With a continuous yield q, c - p = S e^(-qT) - K e^(-rT). S e^(-0.03) = 40 x 0.970446 = 38.818 and K e^(-0.05) = 42 x 0.951229 = 39.952. The difference is -1.13. The 0.05 option ignores the dividend yield, and the -3.18 option does not discount the strike.

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