Consider a one-period binomial model as in Problem 1 with So = 4, u = 2, d = 1, and =. Consider a European call option with strike price K = 5 and maturity at time 1. (a) Show that the time zero arbitrage-free price of this European call option is 1.20. (b) Consider an agent who begins with wealth Xo = 0 and at time zero buys Ao shares of stock and I' options. The numbers Ao and I can be either positive or negative or zero. This leaves the agent with a cash position -4A0 - 1.200. If this is positive, it is invested in the money market; if it is negative, it represents money borrowed from the money market. At time one, the value of the agent's portfolio of stock, option, and money market assets is X = AS + Io(S 5)+ (4A, +1.200). Assume that both S and S have positive probability of occurring. Show that if there is a positive probability that X is positive, then there is a positive probability that X is negative. In other words, one cannot find an arbitrage when the time-zero price of the option is 1.20.