# 留学经济作业代做 Asset Economy Exercises ## Asset Economy Exercises

Exercise 3.2 from Lengwiler. Suppose there are two states and three Önancial assets, a risk-free bond with state-contingent cash áows (100; 100), a risky bond

that pays only in state 2, with cash áow (0; 100), and a share with cash áow(20; 35). Can you Önd a portfolio containing only shares and risky bonds that

reproduces 40 risk-free bonds?

1. ### Exercise 3.3 from Lengwiler. Consider a situation in which there are Öve states, and suppose you can observe the prices of the Arrow securities. They are  (0:1225; 0:2451; 0:3676; 0:0613; 0:1838). 留学经济作业代做

(a) Compute the price of a risk-free bond and the risk-free rate of return.

(b) What are the risk-neutral probabilities of the Öve states?

(c) How much does a hypothetical asset cost with cash áow (5; 5; 2; 7; 4)?

1. Exercise 3.4 from Lengwiler. Consider a two-period economy with Öve possible states in the future. There are no markets for Arrow securities, so you can

not observe the Arrow security prices. Yet, you can observe the prices of the following Önancial assets:  留学经济作业代做 The option on the share of company X is a call option with exercise price 2.

1. (a) Is the market complete?

(b) Compute the prices that Arrow securities would have if they were traded.

(c) Are there arbitrage opportunities in this market? Prove your claim.

(d) Compute the risk-free rate of return.

(e) Compute the risk-neutral probabilities.

(f) Consider a call option on a share of company Y with exercise price 5.

What state-dependent cash áow does this option have? How much should it cost?

1. ### Consider an economy with one good and two states.  留学经济作业代做

(a) Suppose we have two Önancial assets and the asset markets are complete.

Show that a consumerís budget constraints for s = 0; 1; 2, can be collapsed into one budget constraint

Q1 x1 + Q2 x2 + x0 = Q1 !1 + Q2 !2 + !0

Determine Q1 and Q2: (b) Interpret the budget constraint in a: through Arrow security prices.

(c) Suppose we have one Önancial asset hence the asset markets are not complete. Show that a consumerís budget constraints for s = 0; 1; 2, can be collapsed into two budget constraint Determine P1 and P2: (you may use some particular values for r1; etc.)

1. Suppose we have 2 Önancial assets and the asset markets are complete. Formu late the portfolio choice problem. That is consider the agent with today wealth

w0;who has access to the Önancial markets with two assets with the payo§s with the prices of the assets (q1; q2): (you may use some particular

values for r11; etc.) At date 0 the agent can decide on asset holdings (z1; z2)  留学经济作业代做

which determines his t = 1 wealth, call those w1 and w2 in the corresponding states.

(a) Derive the agentís budget constraint, that is the combinations of w1 and w2 that are feasible given the markets and the initial wealth.

(b) Connect the no arbitrage condition to the slope of the budget constraint. 