An option has strike price of $21 and 7 months to expiry.The current price of the underlying share is $45 and its volatility (sigma) is 21%.The riskfree rate of interest is 4% per annum. Calculate d2 for this option. [your answer should have at least 2 decimal places]

Question

BlackTom AI · Accepted Answer

d2 = d1 − σ√T from the Black–Scholes model, so first compute d1 then subtract σ√T.

Relevant concepts:
- Black–Scholes d1 and d2 formulae:
  d1 = [ln(S/K) + (r + 0.5σ^2)T] / (σ√T)
  d2 = d1 − σ√T
- Convert time to expiry to years: 7 months = 7/12 ≈ 0.5833333 years.

Step-by-step calculation with intermediate values:
1. Inputs: S = 45, K = 21, σ = 0.21, r = 0.04, T = 7/12 = 0.5833333.
2. Compute ln(S/K): ln(45/21) = ln(2.14285714) ≈ 0.76209.
3. Compute σ^2 and half: σ^2 = 0.21^2 = 0.0441; 0.5σ^2 = 0.02205.
4. Compute (r + 0.5σ^2)T: (0.04 + 0.02205) × 0.5833333 = 0.06205 × 0.5833333 ≈ 0.0361958.
5. Numerator for d1: ln(S/K) + (r + 0.5σ^2)T = 0.76209 + 0.0361958 = 0.7982848.
6. Denominator σ√T: √T = √(0.5833333) ≈ 0.7637626, so σ√T = 0.21 × 0.7637626 ≈ 0.16038915.
7. Compute d1: d1 = 0.7982848 / 0.16038915 ≈ 4.97717.
8. Compute d2: d2 = d1 − σ√T = 4.97717 − 0.16038915 ≈ 4.81678, which rounded to two decimal places is 4.82.

Why this is correct:
The Black–Scholes definitions were applied directly with correct unit conversion for time and precise intermediate arithmetic; subtracting σ√T from d1 yields d2. There are no alternative multiple-choice options to compare here; common mistakes would be omitting the time conversion or using σT instead of σ√T, which would produce incorrect (much smaller) values.

Conclusion: d2 ≈ 4.82, matching the provided answer.

An option has strike price of $21 and 7 months to expiry.The current price of the underlying share is $45 and its volatility (sigma) is 21%.The riskfree rate of interest is 4% per annum. Calculate d2 for this option. [your answer should have at least 2 decimal places]数值题

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