FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model
For a European option, d1 is calculated as 0.45. The volatility is 30% per year and the time to expiry is 4 years. What is d2?
d2 is -0.15. The difference between d1 and d2 is σ√T, which is 0.30 × 2 = 0.60 for four years. Subtracting this from d1 of 0.45 gives -0.15. Using σ alone, without scaling by the square root of time, is the common error.
- A0.15
- B0.09
- C1.05
- D-0.15Correct
Explanation
d2 = d1 - σ√T = 0.45 - 0.30 × √4 = 0.45 - 0.60 = -0.15. Subtracting only σ gives 0.15, which ignores the time scaling. Subtracting σ²T = 0.36 gives 0.09, and adding 0.60 gives 1.05.
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