Q-34. Solution: D

u = e^(σ√Δt) = e^(18.25%×√1) = 1.2 d = e^(-σ√Δt) = 0.83
Next, we project the various paths the stock's price can follow over the 3 year period. The stock has 4 potential ending values:
S_uuu = $75 × 1.2 × 1.2 × 1.2 =$129.60
S_uud = S_duu = S_udu = $75 × 1.2 × 1.2 × 0.83 =$89.64
S_udd = S_dud = S_ddu = $75 × 1.2 × 0.83 × 0.83 =$62.00
S_ddd = $75 × 0.83 × 0.83 × 0.83 =$42.89
The only point at which the option finishes in the money is after 3 upward moves, with a probability of 60%^3 = 21.6%.
The value of the option today is therefore (129.60 – 90) × 21.6% × e^(-5%×3) = 7.36.