Question A.2 Consider three assets with returns in three states of nature as follows: 2 2 3 T1: 4 3T2: O a T3: 2 2 3 k where k 2 0 is a parameter. (i) Examine whether or not this asset structure is incomplete for some values of the parameter k. [5 marks] (ii) Let k = 0. Examine whether or not the following vector of prices (corresponding to assets r1, T2 and r3 respectively) has the no arbitrage property ql 2 12 = 7 (13 1 [5 marks] (iii) Let k = 4. If (11 = q2 = 3, nd the price (13 of the asset '33 so that the vector of the three asset prices has the no arbitrage property. [5 marks] (iv) Let k = 1. If I11 = 2, (12 = 3, (13 = 2. Construct an option of your choice on the asset T3 and nd its no arbitrage price. [5 marks]