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Answers for “在布莱克-斯科尔斯-默顿公式中,中间变量 d_1 和 d_2 是如何计算的?”

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The intermediate variable d1d_1 is calculated using the formula d1=ln⁡(S0/X)+(r+σ2/2)TσTd_1 = \frac{\ln(S_0/X) + (r + \sigma^2/2)T}{\sigma\sqrt{T}}. The intermediate variable d2d_2 is not computed from scratch; instead, it is derived directly from d1d_1 using the relationship d2=d1−σTd_2 = d_1 - \sigma\sqrt{T}.

Conditions: S0>0S_0 > 0 and X>0X > 0 to evaluate the natural logarithm ln⁡(S0/X)\ln(S_0/X).; σ>0\sigma > 0 to serve as a valid denominator.; T>0T > 0 for the square root T\sqrt{T} to be meaningful.

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To compute d1d_1 and d2d_2, first convert the time to maturity into years. Then substitute the given parameters into the formula for d1d_1: d1=ln⁡(S0/X)+(r+σ2/2)TσTd_1 = \frac{\ln(S_0/X) + (r + \sigma^2/2)T}{\sigma\sqrt{T}}.

Conditions: The parameters are S0=60S_0=60, X=65X=65, r=11%r=11\%, σ=45%\sigma=45\%, and maturity is 4 months.; Time TT must be expressed in years, so T=4/12T = 4/12.; Values of d1d_1 and d2d_2 must be rounded to the nearest hundredth before table lookup.