4. (8 marks) Lattice properties. Let ytree (S, K1, K2, t) be the solution from a binomial tree (lattice) pricer, for an European butterfly with constant volatility o, risk free interest rate r and strikes K1, K2. Assume that the parameters u, d, p* are given, with risk neutral probability 0

0 is a constant, then ytree (ASM, AK1, K2, t) = av tree (Sm, K1, K2,t), j = 0,... , n, m = 0,...,N 1. (Hint: use induction. Note that the algorithm proceeds backwards from N + 0, so that the base case is n = N.) 4. (8 marks) Lattice properties. Let ytree (S, K1, K2, t) be the solution from a binomial tree (lattice) pricer, for an European butterfly with constant volatility o, risk free interest rate r and strikes K1, K2. Assume that the parameters u, d, p* are given, with risk neutral probability 0

0 is a constant, then ytree (ASM, AK1, K2, t) = av tree (Sm, K1, K2,t), j = 0,... , n, m = 0,...,N 1. (Hint: use induction. Note that the algorithm proceeds backwards from N + 0, so that the base case is n = N.)