174mt1 - year. What is the the correct price of a one year...

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Math 174 Midterm 1 February 2, 2011 Do the following problems. Show all your work. Partial credit will be given only for exhibited work. Good Luck! 1. ( 20 points) (a) (6 points) Graph a bull spread with a stock S as underlying made with calls and strike prices K 1 and K 2 , with K 1 < K 2 , and expiration date T . (b) (6 points)Give explicit formulas, as a function of S T and the other data, for the profit of the spread (assume the spread costs nothing). (c) (4 points)How should the graph be shifted if we include the cost of creating the spread? (d) (4 points) What is the profit from the spread when K 1 = 20 and K 2 = 30 when the S T = 19, S T = 25 and S T = 40. 1
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2. ( 20 points) (a) (8 points) Explain what an arbitrage is. (b) (12 points) The spot price on an asset is $ 50 per unit. The risk- free interest rate is 10%. Suppose the six month forward price is $51.50. Is there an arbitrage? If so, explain how you would exploit it to make money. 2
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3. (25 points) (a) (6 points) The price of a European call option with strike price $50 on a non-dividend-paying stock is $6. The stock price today is $51 and the risk-free rate is 6%. The option matures in one
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Unformatted text preview: year. What is the the correct price of a one year European put option with the same strike price? (b) (13 points) What is a general formula for a lower bound on the price of a put with strike price K, maturity T, and risk-free rate r? Give an arbitrage argument to prove this lower bound. (c) ( 6 points) What is the correct lower bound for the price of the put in the case where the stock gives dividends of total present value D? . 3 4. (10 points) The risk-free interest rate is 10% with quarterly compound-ing. What is the equivalent rate for continuous compounding. 4 5. (15 points)The risk-free rates (with continuous compounding) for de-posits are 5% for 6 months, 6% for one year, and 7% for 18 months. What is the theoretical price today of a bond with 100 dollar par value that gives coupons semiannually at annual rate of $8 ? Assume the bond matures in 18 months. 5 6. (10 points) The one year zero rate is 5%. The two year zero rate is 6%. What is the one year forward rate? 6...
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This note was uploaded on 01/30/2012 for the course MATH 174 taught by Professor Donblasius during the Spring '11 term at UCLA.

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174mt1 - year. What is the the correct price of a one year...

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