I need help answering the following questions!

1. Consider a two step binomial tree model. In the class we used induction to derive the pricing formula of ft and fa fu = e-rot[pfuu + (1 -p) fud] fa = e-rot [pfud + (1 - p)fad]. Of course we can go through the full no-arbitrage derivation and get the same results. Assume that we do this. (a) What are the expressions of the stock positions Au and a at the two nodes at t = 1? (b) Are they the same with A? What does this mean for the construction of a dynamic riskless hedge? 2. In a binomial model with where the underlying pays no dividend, the risk-neutral proba- bility is erot _ -d P = u - where u = e"vat and d = 1/u. (a) Notice that p can take many values. What is the condition for ot such that p and 1 - p constitute a probability distribution? (b) When there is a continuous-time dividend rate q, the risk-neutral probability is e(T-q)ot - d P = u -d In other words, in the p-world, the stock price must move up with a smaller prob- ability to justify the valuation of the risk-neutral investor (or the expected return from the stock must be less). Does this make sense? What is the economic intuition of this result? 3. Consider a derivative with two i.i.d. underlying stocks S and $2 with volatility of and 02. The payoff is max{ (ST + S7)/2 - K, 0}. (a) If you want to price this derivative with a 2-step binomial tree, how many possible values of date T option payoff do you have? What if it is a n step binomial tree? (b) Now assume you want to price a derivative with three underlying stock prices using a n step binomial tree. How many possible values of terminal payoff do you have? What if you have 10 underlyings? 40? (c) What does this say about the limitation of the application of the binomial model