BUSI 588 Midterm

BUSI 588 Midterm - N Midterm exam Derivative securities Fall 2008 r Problem 1 Tom Brady(25 points Tom Brady is seriously considering giving up his

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Unformatted text preview: N... . Midterm exam Derivative securities, Fall 2008 r Problem 1 - Tom Brady (25 points) Tom Brady is seriously considering giving up his full—time job now that he has learnt about trading financial securities. There are only so many Superball rings one can enjoy. Taking long and short positions in calls and puts definitely beats throwing a ball around on Sundays and some Monday nights. Given his experience, he has decided to start trading on securities whose cash flows depend on the outcome of sports competitions. He believes that the world over the next year will basically boil down to either the Patriots wins the Superball (again); or (ii) the Patriots do not win the Superball. For sake of argument, let’s call outcome the u-state, and outcome (ii) the d-state. After some hard analysis he concludes the values of the Patriots Corp, a very liquid stock traded on the the Boston Stock Exchange, are given by the following table. The column Price refers to the last traded price for the stock. d state u state Price Patriots Corp 90 150 100 Tom Brady estimates the probability of the Patriots winning the SuperBall at 50%. There is a riskless asset that pays a riskless return of 10%. Peyton Manning, a fierce albeit weak football competitor, has started emulating Bradys’s steps in financial markets, and has actually opened up a market that sells a particularly interesting derivative security. This derivative security is called GoColts, and pays $100 in the d state, nothing ($0) in the u state. /l./ What do you think the price of the GoColts security ought to be in the absence of arbitrage n- opportunities? Use the risk-neutral pricing technique to come up with your answer. How would you interpret the risk—neutral probability of the up state? /Manning is creating a market for this security quoting a bid price of $50 and an ask price of $51 for it. Can you make arbitrage profits by trading on Patriots Corp, riskless bonds and/ or GoColt securities? Please be specific as to the trades you would suggest. A Tom Brady realizes he was being too naive. A better approximation to uncertainty over the next year is to assume that either the Patriots win the NFC title and the Superball; (ii) the Patriots wins the NFC title, but lose the Superball; (iii) the Patriots do not win anything this year. Call outcome the u-state, outcome (ii) the m-state, and outcome (iii) the d-state. After further analysis he concludes the values of the Patriots are given by the following table. d state m state u state Patriots Corp 90 100 150 Patriots Corp. is still trading at $100. The riskless rate is still'10%, and the GoColts securities pay $100 if and only if state d occurs. You also know that a call option on the Patriots Corp with a strike price of $100 is selling for $12.63. / What can you say about the price of the GoColt securities in this trinomial world? \ © Diego Garcia, Kenan—Flagler Business School Page 2 of 4 ,yoA+ /.lB+SOC (7 st+m6+0930 70/5 +1.10; keg 5» IJ'O \\ Midterm exam Derivative securities, Fall 2008 Problem 2 - The hedgehog (25 points) Vish Anand is getting ready to try his best hedgehog defence in financial markets. In particular, Vish has turned into an avid trader in FX markets, particularly on the euro/ dollar markets. In his Bloomberg screen Vish spots the following information. Maturity Forward price (dollars/ euro) 0.5 1.49263 1 1.47115 You also have the following information on T-bill rates (in annual terms) from both the US and Europe. Maturity US rates Euro rates 0.5 1% 2% 1 2% 4% Vish is somewhat nervous: risk—free rates, forward prices, .. . . This is all very confusing!? Can you estimate the current spot price for euros? Vladimir Krammik, a close friend of Vish, claims that based on the forward prices on the dollar, it must be that market expects the US dollar to depreciate. How else can Vish explain the downward movement in forward prices? Do you agree with Vladimir? 3. You estimate the volatility of the dollar/euro exchange rate to be around 30% (in annual terms). Using the Black-Scholes model, can you estimate the value of an at-the—money call option with a one year maturity? What would be the replicating portfolio for this call (according to the Black—Scholes model)? 4. If Vish owned 40 at-the-money call options, how would he hedge his portfolio by trading in the underlying asset? How about if he had sold 40 at—the—money calls and 20 at—the-money puts? ’- (rfir I © Diego Garcia, Kenan—Flagler Business School ‘ Page 3 of 4 Midterm exam Derivative securities, Fall 2008 Problem 3 - Goldberg Variations (25 points) Goldberg Corp. is a NASDAQ firm currently trading for $100. You know that over each of the following three months the Goldberg stock can go up by 20% (with a 70% probability) or down by 10% (with a 30% probability). The annual risk-free rate is 10%. You are working for Golden Sacks, and you have dealing with an important client, J .S.Bag. He is neither bearish nor bullish on Goldberg, so he would like to buy a strangle on the firm. In particular, he would like to get the payoffs from buying a put option with a strike of $90, and buy a call option with a strike of $110. Both options have a 3-month maturity. 1. Construct a 3-step binomial tree for the evolution of the stock and estimate the value of the strangle. 2. Given that there are no options traded on Goldberg, Golden Sacks would have to replicate the payoffs from these options. How can you replicate the payoffs of the strangle in this 3-step binomial tree? Be as specific as you need to when describing that trades that you would make (at the current moment, as well as in future dates). 3. Suppose that the stock went up during the first period, so Goldberg is trading at $120. Further suppose Tomas Albinoni, a well-known options trader, quotes a bid price for the strangle of 17.50, and an ask price of 17.70. Is there an arbitrage opportunity? How would you take advantage of it? Be as specific as you can in terms of the trading strategy you would recommend. 9. Aljo‘f- [\JQDj3OfZL ‘1} Aida 11/65 5.977VV © Diego Garcia, Kenan-Flagler Business School Page 4 of 4 ...
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BUSI 588 Midterm - N Midterm exam Derivative securities Fall 2008 r Problem 1 Tom Brady(25 points Tom Brady is seriously considering giving up his

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