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

A non-dividend-paying stock trades at 50. A European option has strike 50 and one year to expiry. The continuously compounded risk-free rate is 4% and volatility is 25% per year. What is d2 in the Black-Scholes-Merton formula?

d2 equals 0.035. First d1 = (0.04 + 0.03125)/0.25 = 0.285, since ln(S/K) is zero. Then d2 = d1 minus σ√T = 0.285 - 0.25 = 0.035. The value 0.285 is d1, not d2.

  1. A0.285
  2. B0.035Correct
  3. C-0.035
  4. D0.535

Explanation

d1 = [ln(50/50) + (0.04 + 0.25²/2)(1)] / 0.25 = (0.04 + 0.03125)/0.25 = 0.285. d2 = d1 - 0.25 = 0.035. The option 0.285 is d1, and 0.535 comes from adding the volatility instead of subtracting it.

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