Homework 4 due Mar 3 Wednesday K Foster, Options & Futures, Eco 275, CCNY, Spring 2010

 

You are encouraged to form study groups to work on these problems.  However each student must hand in a separate assignment: the group can work together to discuss the papers and comment on drafts, but each study group member must write it up herself/himself.  When emailing assignments, please include your name and the assignment number as part of the filename.

Please write the names of your study group members at the beginning of your homework to acknowledge their contributions.

1. Please complete Assignment Question 8.23 in Hull.
2. Please complete Assignment Question 9.23 in Hull.
3. Please complete Assignment Question 9.24 in Hull.
4. Please complete Assignment Question 9.25 in Hull.
5. A portfolio consists of two options on the same underlying stock, with the same expiration date in three months.  The stock currently trades at $85.  One option is a call with strike price of $87.  The other option is a put with strike price of $84.  Show the payoff graph for the portfolio.
6. An insurance company wants to hedge its position against hurricanes.  The company believes that a Category-3 hurricane hitting a large city will cost it $500,000,000.  It can buy "catastrophe bonds" that each pay out $2,500,000 in the event of a Cat-3 hurricane hitting the city.  Each bond costs $10,000.  The company would like to hedge at least 50% of its exposure.  Should it buy or sell the catastrophe bonds?  How many?  What is the total cost?  Or, the company could hedge using the city's municipal bonds, which would decrease in price if a hurricane struck.  Explain the advantages and disadvantages to this alternate hedging strategy.
7. A riskless bond pays 4% per year (compounded continuously).  A stock has 25% volatility over a year. The stock's current price is 80. Your portfolio is long with 2 puts with strike prices of 75 and 70 and long one call with a strike price of 82.  All these options have three months to expiry. 
1. Draw a payoff graph for the portfolio.
2. Next a short call position, with an at-the-money strike, is added to the portfolio (same expiry).  Draw the new payoff graph for the portfolio.
3. Then a short put position is added, with a strike of 78 and 3 months to expiry.  Draw the new payoff graph.
8. A bank has written 1000 calls on stock ABCD.  These calls expire in 6 months and have a strike price of 15.  ABCD's stock currently trades at 16.  The portfolio of calls is currently worth 1956.88.  The bank believes that the stock will be less volatile in the future: five percentage points less volatile than current option prices imply.  What strategy of long/short positions in options, riskless bonds, or stock would allow the bank to profit from this knowledge?  Explain how risky each strategy is.