Homework 2

due Feb 17 Thursday

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. How did your portfolio from last week do?  What is it worth now?  How much profit/loss did you make?  Can you plot its payoff graph?  Discuss.
  2. Complete Assignment Question 3.23 in Hull.
  3. Complete Assignment Question 3.24 in Hull.
  4. Complete Assignment Question 4.24 in Hull.
  5. Complete Assignment Question 4.25 in Hull.
  6. Complete Assignment Question 4.26 in Hull.
  7. Complete Assignment Question 4.27 in Hull.
  8. Complete Assignment Question 4.28 in Hull.
  9. What are the LIBOR rates currently?  Using these rates calculate the value (under continuous interest) of a bond paying $1m in 3 months, of a bond paying $3m in 6 months, and of a bond paying $10m in a year.  Compare these with Treasury rates (calculate the three bond prices again).
  10. What are current fixed rates on 30-year home mortgages?  Suppose you want to buy a property for $300,000.  What series of 30 equal payments would have a present value of $300,000 (assume annual compounding)?  Suppose compounding were monthly (12 per year so 360 payments over 30 years)
     what level payments would have a $300,000 present value?
  11. Suppose a mortgage lender offered an initial 'teaser' where the payments for the first 5 years would be 150 bp less than the fixed rate but then jumped up to a higher rate for the remaining 25 years.  What must this higher forward rate be, to have the same $300,000 present value?
  12. A bond pays $7m in ten years.  Its current price is $4.89m.  What continuously compounded 10-year zero rate is implied?  What semiannual 10-year zero rate is implied?  A different bond (paid by the same entity with identical risk characteristics) pays $4m in five years.  Its current price is $3.27m.  What continuously compounded 5-year zero rate is implied?  What semiannually compounded 5-year zero rate is implied?  What is the year-5-to-year-10 forward rate (continuously and semiannually)?
  13. The interest rate jumps by 15 basis points.  What would be the new prices on the two bonds from the problem above?

 

Chapter 4 is one of the most important and difficult so you should ensure that you are able to answer the text's Q 1-23 as well.