Question: 2. Consider a one-period binomial model as in Problem 1 with SD = 4, u = 2,d = l and 2: 'r = i. Consider

2. Consider a one-period binomial model as in Problem 1 with SD = 4, u = 2,d = l and 2: 'r = i. Consider a European call option with strike price K = 5 and maturity at time 1. (a) Show that the time zero arbitragefree price of this European call option is 1.20. (b) Consider an agent who begins with wealth X0 : 0 and at time zero buys AD shares of stock and To options. The numbers A0 and F0 can be either positive or negative or zero. This leaves the agent with a cash position 74AD i 1.201}. 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 5 X1 = A081 + F0(Sl 5)... 1(4A0 +1.20%). Assume that both Si' and 8'11 have positive probability of occurring. Show that if there is a positive probability that X1 is positive, then there is a positive probability that X1 is negative. In other words, one cannot nd an arbitrage when the timezero price of the option is 1.20

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