Midterm Exam

 

K Foster, Options & Futures, Eco 275, CCNY, Spring 2010

 

 

  1. (10 points) You're going to buy corn futures; each full-sized contract is 5000 bushels, while mini-contracts are 1000 bushels (delivered to a few locations in Illinois).  Currently the contract for July 2010 delivery (on the 14th of that month) trades at 375 (cents per bushel). 
    1. How much does a single full-sized contract cost?  A mini-contract?
    2. Given interest rates of 2.5%, what range of prices would not present arbitrage opportunities?
    3. Initial margin is $1350 so assume you buy one contract with only that margin amount.  The maintenance margin is $1000.  How large of a price decline would trigger a margin call?

 

  1. (20 points) You have a portfolio with calls and puts on oil contracts; all of these options are European.  The current oil price is $80.68/barrel.  You are long 10 calls with strike of 82 and short 8 calls with strike of 84.  (Contract size is 1000 barrels in each; each option brings the right but not the obligation to buy 1000 barrels.)  You own 5 puts with strike price of 81 and 5 puts with strike price of 80.  You are short 7 puts with strike prices of 83. 
    1. Draw the payoff graph for your portfolio.

 

    1. If you bought 10,000 barrels (or 10 contracts) at a price of 80.50/barrel, how would the payoff graph change?

 

  1. (25 points) You are considering whether to buy an at-the-money European put, expiring in a month, on a stock that is currently worth 50.  After one month assume the stock will be worth 55 or 45.  The risk-free rate is 2%.
    1. What are the risk-neutral probabilities of the stock rising or falling?
    2. What is the delta for the put?
    3. What is the fair value of the put?

 

  1.  (20 points) The Greek government has seen prices of its bonds fall dramatically.  Consider two (fictitious) bonds; both pay 100 semi-annually.  One is an on-the-run 5 year bond with just 1.5 years remaining (3 remaining payments); the other matures in 3 years and also pays 100 semi-annually. 
    1. As of September 2009, the first bond traded at a price of 292.65.  The second bond traded at a price of 662.61.  Assuming discrete semi-annual compounding, what was the implied zero rate for 1.5 years?
    2. What was the forward rate from 1.5 to 3 years?
    3. By March 2010 (6 months late), Greece's fiscal crisis had begun worrying the financial markets so bond prices plunged.  Now the same first bond from part (a), with just 2 payments left now, trades at a price of 192.74; the second bond with 2.5 years remaining trades at 463.27.  What is now the implied zero rate for 1 year?
    4. What is the forward rate from 1 to 2.5 years?
    5. Actual Greek bonds saw the yield curve compact, as short rates rose substantially while longer yields rose by less; the graph below (data from Greek Central Bank) shows yields on 3 – 30 year bonds.  Explain why this might be so.

 

    1. How has the duration of these bonds changed?