My solution to the problem was: d1 = [ln(34.55/40) + (2.5%+0.5*0.1^2)*3]/0.1*sqrt(3) = -0.32604 ≈ -0.33 d2 = d1 – 0.1 * sqrt(3) = -0.4992 ≈ -0.50 Φ(d2) = Φ(-0.50) = 1-Φ(0.50) = 1- 0.69146 = 0.30854 Φ(d1) = Φ(-0.33)=1- Φ(0.33) = 1- 0.62930 = 0.3707 c_t = 34.55 * Φ(d1) - 40 * exp (-0.025 * 3) * Φ(d2) = 1.36 However, the memo gives a slightly higher answer of 1.3998 and different Φ values . Not sure how we are differing. Please help.
The Black-Scholes option pricing formulae are very sensitive to the rounding of d1 and d2. Rather than use approximate values for d1 and d2 you can use NORM.S.DIST(x,TRUE) in Excel to get accurate values for \(\Phi(x)\).
