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MATH 2281 3.0MW (Financial Economics)
Assignments - Winter 2011


Assignments and their solutions will be posted here as they become available.

Note that access to the assignment solution pages has been withdrawn. If you took this course and now need access to those pages, feel free to contact me.

Practice problems II

I was asked for additional problems, similar to some on the midterms. You can try the following if you like. (Not to be handed in).
problem set
Solutions
[Both modified slightly on Apr 11]

Practice problems I

Not to be handed in. Solutions

Assignment 6

due Friday April 1, 2011 (in class, or by 5pm in the assignment box)

The following problems all refer to the setup of the 11.16 in the book, which you studied earlier on Assignment 4. In particular, you have an 8-period binomial tree, with expiration T=1, initial stock price S=100, interest rate r=0.08, volatility sigma=0.3; In assignment 4 you obtained u=1.112 and d=0.899 using the CRR calibration. You will be looking at European and American calls, with strike K=95. You will look at two dividend rates, div=0 and div=0.05; You may wish to start with the tree you built for assignment 4. Or, if you wish, you may take as a starting point the tree I posted in the solutions to assignment 4, but you do that, you will need to modify it to incorporate dividends.

  1. On assignment 4 and 5 you computed the European and BSM prices when del=0. Now find them both when del=0.05
  2. Take div=0. Verify that there is no early exercise and find the American option price in this case.
  3. Take div =0.05 and find the American option price. Find the early exercise premium. Indicate at which nodes it is optimal to exercise early.
  4. Take div=0.05; Which of the two American option prices 15.0 or 15.5 gives an arbitrage you can exploit by buying the option? Describe the cash flows and give the optimal exercise time, if the actual sequence of stock prices changes observed is uuuuudud.
  5. Take div=0.05; Which of the two American option prices 15.0 or 15.5 gives an arbitrage you can exploit by selling the option? Describe the cash flows, if the actual sequence of stock prices changes observed is uuuuudud, and if the buyer exercises after 4 periods. Do the same if the buyer holds the option to expiration.
Solutions and accompanying spreadsheet

Assignment 5

due Monday, March 14, 2011 (in class, or by 5pm in the assignment box) Solutions and accompanying spreadsheet
All 5 questions were graded, for a total of 50 marks.

Assignment 4

due Friday, March 4, 2011 (in class, or by 5pm in the assignment box) Solutions and accompanying spreadsheet
All 6 questions were graded, for a total of 60 marks.

Assignment 3

due Monday, February 7, 2011 (in class, or by 5pm in the assignment box) Solutions (corrected).
All 5 questions were graded, for a total of 50 marks.
A question came up about problem 5.16 and whether the factor in the denominator is really 917.57 (the futures price) or 875 (the current level of the index). In fact the solution I gave is correct, and is consistent with the formula given in the notes. But I realize I never actually proved this formula for you. I will try to write up a derivation over reading week.

Assignment 2

due Monday, January 31, 2011 (in class, or by 5pm in the assignment box) Solutions
5 questions were graded (5.8, 6.9, 7.10, 7.12, 8.14) for a total of 50 marks.

Assignment 1

due Friday, January 21, 2011 (in class, or by 5pm in the assignment box)
Note that several of the questions require you to read portions of the text, to understand what is being asked, eg bid/ask prices, asymmetric butterfly spreads, and the examples of chapter 4. Solutions
7 questions were graded (1.6, 2.2, 3.3, 3.6. 3.14, 3.17, 4.3) for a total of 70 marks.