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.