Setup: • assume that there are three states of the world {s1, s2, & 33}, all with equal likelihood and that the stock price for xyz corp takes the values {2, 3, & 5} across these three scenarios, respectively. • you also observe the following prices in the market: - the stock is trading at $2.79. - a derivative contract that pays off the square of the stock price (i. e. payoffs of: {4, 9, & 25}) is trading at $9.63. - a put option with a strike of 4 that is trading at $0.99. (a): for the one-period model described above, find the state prices {v1, v2, & 03} as well as the risk-neutral probabilities {91, 42, & q3}. (b): compare the objective probabilities (i. e. equal likelihood) with the risk-neutral probabil- ities found in (a). are they the same or different? why? (c): calculate the price of a risk free one period zero coupon bond (assume $100 face). (d): calculate the forward price of the stock for a 1 period forward contract. (e): using expectation pricing, find the price of an "up market" binary contract that pays off if the stock is greater than or equal to $3 (i. e. payoff = $1 if xyz > $3; $0 otherwise). (f): explain why you are not able to hedge the contract in (e) with only a portfolio of the stock and the zero coupon bond. (g): assume you can only invest in xyz and the zero coupon bond. if your utility function is u (rport) = rport - 0.2rport, where r port is the portfolio rate of return. set up the portfolio optimization problem to determine the percentage of your wealth to invest in xyz. derive a system of equations that will allow you to solve for the optimal portfolio weights (you do not have to actually solve them). (*): suppose someone was willing to sell you the "up market" binary contract in (e) for $0.25. construct a portfolio to take advantage of the arbitrage profit. what is your risk in this position?