- Stochastic Discount Factors 19 Marks There Are Two Agents In The Economy Both Have Utility Of Income Function V W 1 (296.52 KiB) Viewed 12 times
Stochastic Discount Factors (19 marks) = There are two agents in the economy, both have utility of income function v (w)
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Stochastic Discount Factors (19 marks) = There are two agents in the economy, both have utility of income function v (w)
Stochastic Discount Factors (19 marks) = There are two agents in the economy, both have utility of income function v (w) = In(w). Current consumption does not enter agents' expected utilities; they are inter- ested only in consumption at date 1. At date 1 the economy can be in state 1 with probability #₁ = or in state 2 with probability 72 = 3. In state 1 agent A receives 6 units of wealth, in state 2 he receives 3 units. Agent B receives 12 units of wealth in either state. a. (7 marks) Compute the equilibrium prices of wealth, (Arrow security prices), and the equilibrium allocations of wealth for Agents A and B. Hint: the mutuality principle does not provide a simple answer here. You need to set up the optimization problem for each agent, solve for the demands for contingent weath, impose market clearing conditions and solve for the equilibrium prices of wealth in different states (or their ratio). b. (1 mark) Given your answer in a. what should be the equilibrium price of the risk-free bond? c. (1 mark) Calculate the values of the risk-neutral probabilities (ã1, ã₂). Check that these add up to 1. d. (3 marks) Compare the values of the risk-neutral probabilities with the val- ues of the true state probabilites. Should they be the same or not? Explain any discrepacies using the risk aversion of the agents. e. (2 marks) What are stochastic discount factors (SDF) in general and what role do they play? f. (1 marks) Calculate the stochastic discount factors for the two states. g. What relationship between the stochastic discount factors (or their ratios) and the equilibrium allocations of wealth should hold here? State the relationship (2 marks). For which agent does it hold? Check formally using your answers in a. and in f. (2 marks)