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Arrow-Debreu Pricing
a. What is the minimum number of Arrow-Debreu states needed to price: (i) a stock, (ii) a government bond, (iii) an at-the-money vanilla call on the stock, and (iv) a slightly out-ofthe-money vanilla put on the stock? CIRCLE ONE: 1 2 3 4 5 Impossible to answer
b. You are evaluating a really great stock with a current market price of $50. Over the next year, this stock could either double in value, or quadruple in value. Or it can go bankrupt. You can buy bankruptcy protection today for $0.50; this protection would pay you $1 in case the stock is worthless, and of course it pays you nothing if the stock doubles or triples.
The risk-free interest rate is 10%.
i. What is the probability of bankruptcy?
ii. What is the probability that the stock doubles?
iii. What is the probability that the stock quadruples?
What is the implied value of the warrants attached to each bond?
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Suppose that you have an obligation to make payments of $5 million in five years and $5 million in ten years. The yield on a five-year zero coupon bond is 5% and the yield on a ten-year zero coupon bond is 7%. What is the value of this obligation?
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Treasury bonds paying an 8% coupon rate with semiannual payments currently sell at par value. What coupon rate would they have to pay in order to sell at par if they paid their coupons annually?
Use the analytical method and determine the VAR at a probability of 0.05 for a portfolio in which the standard deviation of annual returns is $2.5 million. Assume an expected return of $0.0.
What is ‘Setting Capital Market Expectations’?
What are the Black-Scholes prices of the call and the put? What are the option deltas?
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