Note: Correct answers to later questions are dependent on correct answers to earlier questions.
-Ima Greedy,the CFO of Financial Saving Techniques has been granted options on 200,000 shares. The stock is currently trading at $23 a share and the options are at the money. The variance of the stock has been about .08 on an annual basis over the last several years. The options mature in 3 years and the risk free rate is 4%.
Calculate N(d₁) .

Question

Quizplus · Accepted Answer

First, we need to calculate the value of d1: d1 = [ln(S0/K) + (r + 0.5σ^2)t]/(σ√t) = [ln(23/23) + (0.04 + 0.5*0.08^2)*3]/(0.08√3) = 0.6092 Next, we need to calculate the value of d2: d2 = d1 - σ√t = 0.6092 - 0.08√3 = 0.4154 Now, we need to calculate N(d₁): S1 = S0*exp[(r - 0.5*σ^2)t + σ√t] = 23*exp[(0.04 - 0.5*0.08^2)*3 + 0.08√3] = 29.294 U1 = exp(σ√t) = exp(0.08√3) = 1.2632 B1 = exp(r*t) = exp(0.04*3) = 1.125 N(d₁) = N(0.6092*29.294*1.2632/1.125 - 0.4154*23*1.2632/1.125) = N(33.0822) = 0.6879, which is closest to answer choice D.

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