6. (8 marks Under a recombining arbitrage-free binomial tree model with N steps, let V(i,j), V(i +1, j +1), and V(i+1, j) be the prices of a European option prices at the nodes (1,1),(i+1, j+1), and (i+1, j +1) on the tree, respectively, where 0 Sis NOS; Si. With the notations used in class, explain how do we derive the recursive formula (12) V(ij) = eth[qV (i +1,j +1) + (1 - 7)V(i +1,3)], where 0 si Si,oSiSN - 1, and V(N, 1) = f(Sou'dN->) for 0 ) for 0