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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 ustate, and outcome (ii) the dstate.
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 riskneutral 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 ustate, outcome (ii) the mstate, and outcome (iii) the dstate.
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
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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 Tbill 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 BlackScholes model, can you estimate the value of an atthe—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 atthemoney 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—themoney
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 riskfree 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 3month maturity. 1. Construct a 3step 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 3step
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 wellknown 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, KenanFlagler Business School Page 4 of 4 ...
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