(answer IVa)To determine the replicating portfolio we have to solve the following system of linear equations:
- 0=α S1,u+β M1
- 20=α S1,d+β M1
Subtracting the second equation from the first one yields -20= α (S1,u -S1,u). We thus obtain α= - 20/(120-80) = -1/2. Now we can solve for β (from each of the equations): 0= -1/2 x 120 + β x1 → β=60. The price of the option, at t=0, is thus given by 100 x (-1/2) + 60 x 1=10 euro.