Consider a non-dividend paying share whose price is modelled using a binomial tree. The tree is generated using the algorithm that if St is the share price at time t, then in the next timestep the share price can either be St u or St d, where u > d. The continuously compounded constant risk-free rate of interest is r per unit of time. Suppose a European call option contract and a European put option contract are issued at time 0, on the share with the same strike price K and maturity at time 1. Consider the following three cases: Case 1: K S0 d. Case 2: S0 d < K < S0 u. Case 3: S0 u K. (a) For all three cases defined above, determine (i) the self-financing replicating strategies; [ 6 marks ] (ii) the upfront prices; [ 6 marks ] for the European call option contract and the European put option contract, in terms of S0, u, d, r and K. (b) If c and p are the number of shares required at time 0 for the self-financing replicating strategies for the European call option contract and the European put option contract respectively, show that: c p = 1 for all three cases. [ 3 marks ] (c) Provide an interpretation for the result obtained in part (b). [ 2 marks ] [ Total: 17 marks ]