Problem 3. Options and Risk-Neutral Probabilities. Consider an economy where there are three possible states of the world at t = 1. A security with payoffs 09, 1) = [5, Ii], 15) in states 1, 2, and 3, respectively, has a price of 8 at t = U. A riskfree security has a gross return of 1.1 and a price of 1 at t = U. A call option on the risky security has a strike price of 12 and a price of 1 at t = U. The probabilities of states 1, 2, and 3, repsectively, are 11' = [0.3, [1.4, [1.3). 1. Is the market complete?, If yes, what are the state prices? 2. Price a put option with a strike price of 8. 3. Derive the riskneutral probabilities. 4. Determine the values of the stochastic discmmt factor for each state. . Determine the t = 0 value of the payoffs 5:09, 1] = [7, 3, 5} using: U1 (1] The state prioes. [ii] Riskneutral valuation. (iii) The stochastic discount factor. Do all of these valuations agree