For the question, is it ok to split the split the state price deflator A_2(200) so that it is path dependent? i.e. The state price deflators after one year are: if first move up, second up: A(250)=...=0.742 if first move up, second down: A(200)= [(0.6*0.262)/(0.75*0.25)]/(1.03^2)=0.79027 if first move down, second up: A(200)= [(0.4*0.498)/(0.75*0.25)]/(1.03^2)=1.0014 if first move down, second down: A(250)=...=3.004 instead of A(250)=...=0.742 A(200)=...=0.9 A(250)=...=0.3.004 Thanks!!
For the deflator question on last September's paper (Q6) the examiners accept both approaches. So, presumably using 3 deflators (one at each node) or "splitting" the middle deflator by using two separate deflators at the middle node - one for up followed by down and another for down followed by up - should be fine in any future questions. However, I think you've made a slight error in your calculations for the third deflator, which should be: if first move down, second up: A(200)= [(0.4*0.502)/(0.75*0.25)]/(1.03^2) = 1.13011 The other deflators you state are all correct though.
