Assignment
Question 1.
Suppose that an investor wishes to speculate that IBM's stock price will be unusually level (i.e., will not be very volatile) over the next two months. Would that investor find himself better off going long (or short?) one butterfly spread maturing around that time (two months from now); going short (or long?) one bull spread also maturing two months from now; or going short (or long?) one bear spread maturing a month earlier? Explain intuitively, and illustrate with either (i) a plot of all strategies' payoffs or (ii) a table listing their respective payoffs at maturity.
Question 2.
A U.S. bank enters a 5-year cross-currency interest rate swap, whereby it pays a fixed annual interest rate in Canadian dollars (CAD) and receives the US dollar 3-month T-bill rate. The same bank simultaneously enters into a second swap, with the same notional, but where it receives a slightly higher annual fixed rate in Canadian dollars and pays 3-month USD LIBOR minus a fixed premium.
(i) Please draw a box chart detailing the swap flows.
(ii) Assuming away default risk, what risk(s) does the bank face?
A. FX risk (the CAD may depreciate)
B. FX risk (the CAD may appreciate)
C. Basis risk
D. A and C
E. B and C
Please explain your answer. You may, to do so, use in part the box chart detailing the swap flows that you drew part (i). If you answer C, D or E, please specify what basis risk is the bank facing.
Question 3.
We are in late April 2017 and the current stock price of GE stock is $25.75. Consider the following options portfolio. (i) You sell a June 2017 EOM (end-of-month) put on GE stock with an exercise price of $27.5 per share. (ii) You simultaneously sell a June 2017 GE call with the same exercise price ($27.5). Both options are European.
(a) Graph the payoff of this portfolio at option expiration as a function of GE's stock price at that time. (If you prefer, you may establish a table with the payoffs instead of a graph.)
(b) What will be the profit/loss on this position if GE stock is selling at $28 on the options' maturity date? What if GE shares are trading at $23 that day? June 2017 call and put options mature in 6 months, the annualized 2-month risk-free rate is 1.2%, and the prices obtained by the seller for writing those two options are:
Put = $ 4.71 per share
Call = $ 2.03 per share
(c)What kind of "bet" is this investor making? That is, what must this investor believe about GE's future (i.e., June) stock price in order to justify taking this position?
(Hint: look at the payoffs of your portfolio at maturity)
Question 4.
Consider again the same European put and call options on GE stock from Question 4, each having an exercise price of $27.5 as well as the same expiration date of June 2017. Suppose again that the current price of GE stock is $25.75. Assume again, as in Question 4, that a 6-month riskless investment (i.e., till the options' expiration date) currently yield 1% (annualized).
a. Given this information, is there one (or perhaps more) arbitrage opportunity? If there is a profit opportunity, how would you exploit it? Is it truly riskless? Explain and show your work.
b. What current level of the stock price would rule out any obvious arbitrage opportunity?
Question 5.
A European put option on 100 Toyota ADRs (NYSE; ticker: TM) with strike price $105 matures in 3 months. You expect TM (currently trading at $108) to have annual return volatility of about 25% (annualized standard deviation of returns) in the foreseeable future. LIBOR (the "risk-free" rate proxy you use) is 1.2% per annum for maturities up to 6 months.
(a) Is this European put currently in the money? Why-or why not?
(b) If you decide to carry out a binomial option pricing analysis by subdividing the 3-month time interval into three 1-month intervals, what is the risk-neutral probability of TM going up every month?
(c) What would the value of TM be in the tree after 3 months, in case this ADR's value drops each period (i.e., every month)?
(d) Using risk-neutral valuation and a binomial tree, what is the value of that European put option today? Assume the stock went ex-dividend yesterday and no dividends will be paid in the next 3 months. Show your work.
(e) Suppose that you manage a hedge fund that just wrote a bunch of these TM puts, and you would like to hedge your position until maturity. How many shares should you buy or sell today, and how many will you still be holding 1 month from now? How about 2 months from now? Show your work and explain why you need (or do not need) to rebalance.
(f) Would you be willing to pay more for an otherwise-similar American put on TM? Show your work and explain why-or why not.
Question 6
You work for the corporate treasury department of an oil extraction company located in North Dakota's Bakken (a major U.S. shale oil field). In the past year, spot Bakken oil has generally sold at a discount of about $5 to the spot WTI light sweet crude oil benchmark.
You have been tasked with hedging next year's oil output. Suppose that the term structure of WTI crude oil futures prices is currently contangoed, with a spot price of $48/barrel and a $1/month net cost of carry :
a. Would this strategy be an own-hedge or a cross-hedge? Why?
b. Identify one major pro and one major con of using WTI futures to hedge the firm's exposure.
c. Suppose you get the approval to use WTI futures in order to hedge the company's exposure to Bakken oil price fluctuations. Identify risks associated with using a stack-and-roll strategy of rolling over 1-month futures positions to hedge the company's exposure between now and a year from now.