equity price $52 Exercise price $45 Model predicted up move 15% Model predicted down move 20% Annualized risk-free rate 6.00% The valus of the 1 period put option is?

u=1.15, d=1-0.2 = 0.8 pi = r+1-d / u-d = 0.74286 value at up node = Max (0,45- 52*1.15) = 0 value at down node = Max(0, 45 - 52*.08) = 3.4 value at node = 0 * pi + 3.4*(1-pi) / 1+r = 0.8247 I thought I saw somewhere that 1/u = d , but that isn’t the case here. Can someone comment on this?

Spot on…

Why isn’t the case here? Could someone clarify this please? When do we use u=1/d and vice versa?