The CFO of Financial Savings has just been granted at-the-money options on 200,000 shares.The options expire in three years.The firm's stock is currently trading at $22 a share,the volatility of the returns as measured by standard deviation is 19 percent,and the continuously compounded risk-free rate is 3.6 percent.What is the value of d₁ as it is used in the Black-Scholes option pricing model? A).1842 B).4102 C).4583 D).4927 E).5412

Question

Quizplus · Accepted Answer

d1 = [ln(S0/K) + (r + σ²/2)t]/(σ√t) = [ln(22/22) + (0.036 + 0.19²/2)3]/(0.19√3) = 1.3045 d2 = d1 - σ√t = 1.3045 - (0.19√3) = 0.3555 Using N(d1) = 0.9037 and N(d2) = 0.6388: d₁ = S0*N(d1) - Ke^(-rt)*N(d2) = 22*0.9037 - 22e^(-0.036*3)*0.6388 = 49.27 ≈ 4927. Therefore, the correct answer is D.

The CFO of Financial Savings Has Just Been Granted At-The-Money