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

A stock trades at 80 and pays a continuous dividend yield of 2%. The risk-free rate is 5% continuously compounded. In writing the BSM price of a 2-year European option as e^{-rT}[F0 N(d1) - K N(d2)], what is the forward price F0 (e^{0.06} = 1.061837)?

The forward price is 84.95. With a continuous dividend yield, F0 equals S0 times e raised to (r minus q) times T, so 80 x e^{0.06} = 84.95. Ignoring the dividend yield gives 88.41, and adding the yield to the rate gives 92.02.

  1. A84.95Correct
  2. B88.41
  3. C75.34
  4. D92.02

Explanation

F0 = S0 e^{(r-q)T} = 80 x e^{0.03 x 2} = 80 x 1.061837 = 84.95. Ignoring the dividend yield gives 88.41. Using a negative net rate gives 75.34. Adding r and q gives 92.02.

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