Financial Economics Problems -
1. Explain intuitively the idea of an Arrow-Debreu security. These are not observed in "real" markets, so is the concept useful? What is the link between A-D securities and options?
2. There is an economy with two dates (today and tomorrow), but there are three possible states of the world tomorrow. Consumption tomorrow will be $5, $10 or $15. A security that pays one unit of consumption tomorrow is worth $8 today. The risk-free security pays a gross return of $1.10. A call option on per capita consumption with an exercise price of $12 costs $1. The probabilities of the three states are 0.3, 0.4 and 0.3, respectively. Are the markets compete? If so, what are the state prices?
3. You observe the following assets with the corresponding state-dependent payoffs:
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Securities
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A
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B
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C
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States
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3
|
7
|
8
|
|
1
|
2
|
9
|
|
1
|
16
|
25
|
Is this market complete?
4. There are two time periods (t=0 and t=1) and in the t=1 there is a probability of π = 0.5 that a good state occurs and 1 - pi that a bad period occurs. There are 2 assets: a stock and a bond. The stock sells for pricestock = 2.50 at t=0 and the bond sells for pricebond = 0.90 at t=0. If the stock yields 6 in the good state and 1 in the bad state at t=1 and a bond yields 1 in the good state and 1 in the bad state then answer the following:
a) A call option on the stock with a strike price of K1 = 3 begins to trade. What are the payoffs in the good and bad state at t=1 for the owner of this call option?
b) Similar to part a, what if the strike price is now K1 = 2.50? What are the payoffs?
c) Use the info from part a. Ultimately, I want you to find the price of the option in t=0 (this is question d). However, in order to do this you must first find, what percentage of the portfolio will be in stocks and what percent in bonds?
d) Using info from part a and c, what should the call option trade at in t=0 if there are no arbitrage opportunities?
5. The stock price of a company today is $50. Suppose that, a year from now, the stock is worth either $62 or $40. Assume that the risk-free rate between today and a year from now is 4% annually. Consider a European call option written on 40 shares of this company, which has a $34 strike price and which matures a year from now. What is the value of this call option?
6. Explain how you would use this week's information on options to inform your investment choices. Extra credit points if you could use real data to enhance your answer. If you do not believe it is informative, why not?