I need help to find the risk-neutral probability for states 1,2 and 3
I have two stocks: A and B.
The price of A today is 180 and in a year it will be worth 288 (S1), 180 (S2) or 120 (S3);
The price of B today is 100 and in a year it will be worth 94(S1), 134(2) or 54(S3)
The annual rf rate is 2%
I did the following for stock A: up : 288/180-1= 0,6 down :120/180-1 =-0,3333
Finding prob for s1: (2- (-33,33))/ 60- (-33,33)) = 0,3785
Then tried to solve for p2 and then p3:
PV= (0,3785* 288 + p2*180+ (0,6215 -p2 )* 120)/1,02= 180
These probabilities don't add up when I try to find the price of stock B, so they are clearly wrong. Can you tell me how to find the right probabilities?