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Problem C3: Binomial Trees Consider a stock which currently sells for $105. Assume that during each two-month period for the next four months this share price is expected to increase by 5% or decrease by 5% and the risk-free interest rate is 4% per annum (cont. comp.). Consider a derivative that has a payoff given by the formula (max[(ST103),0])2 where S is the stock price in four months. a. Draw a two-step binomial tree and populate the individual nodes with the share price values at each node. [1 mark] b. If this derivative is of European-style, value the derivative using noarbitrage arguments. [5 marks] c. If this derivative is of European-style, value the derivative using riskneutral valuation. [2 marks] d. Verify whether both approaches lead to the same result. [1 mark] e. If the derivative is of American style, should it be exercised early if the payoff at time t is given by the formula (max[(St103),0])2 ? [2 marks] Note: When you use no-arbitrage arguments, you need to show in detail how to set up the riskless portfolios at the individual nodes of the binomial tree