# MATH 2281 3.00MW (Winter 2012)Financial Economics Course Notes and Topics

Lecture notes are given below, based on last year's version of the course. This year's version will follow them closely, though not everything will be exactly the same.

The Hull book contains much more information than we will go into in class, about the actual operation of futures and options markets, and about the use of futures and options in the world of finance. The course emphasizes mathematical aspects of the subject, and we do that in a bit more depth than Hull. Students are encouraged to read the background information, but doing so is optional (and indicated as such below). Students are responsible for what is covered in class (there is typically more detail given in the textbook).

## Lecture notes and topics

### Forwards and Futures

• Optional reading: Background on forward and futures markets, chapters 1-3
• Optional reading: Review of interest and bonds (ie MATH 2280), chapter 4
• Forward contracts on stocks: Chapters 1.3, 5.1-5.5, 5.7
• Forwards on currency and commodities: Chapters 5.10-5.12
• Forwards on interest rates, and an example of an FRA settled in advance: Chapters 4.6-4.7, 7.1, and part of 7.6-7.7
• Futures contracts: Chapters 1.4, 2.1-2.4, 2.11, 5.8
• Examples: Types of contracts, Canola contract: Chapters 5.9-5.12, 6.1-6.3
Optional examples not covered this year: Index hedging, Bond hedging, Hedge calculations. Chapters 3.5, 6.4

### Options

• Types of options: Chapters 9.1-9.2, 11.2-11.5
• Optional reading: Background on options, chapters 9.3-9.12
• Qualitative properties of options: Chapter 10
• Pricing and Trees: Chapters 12.1, 12.3-12.4, 12.8-12.9
Spreadsheet for European Calls and Puts. (For problems you can use Hull's software, build your own in Excel, or modify my workbooks)
• Risk neutral valuation: Chapter 12.2
• Calibration and the lognormal distribution: Chapters 12.6-12.7 and appendix to Chapter 12, 14.1-14.4
Optional reading: Monte Carlo simulation, Chapter 20.6
Optional reading: Alternate calibrations, Chapter 20.4
• Dividends: Chapter 20.1 and 20.3
• Black-Scholes-Merton and spreadsheet: Chapters 14.7-14.9 and appendix to Chapter 14. Parts of Chapter 14.12
• American options and spreadsheet: Chapter 12.5 (and parts of Chapter 20 referred to above).
• Optional reading: Complete markets
• Option sensitivities: Chapter 18 (you are responsible for the definitions, and then for the formula for Delta and its application to hedging).
• Estimating volatility: Chapter 14.4
• Optional reading: Options on other assets
• Optional reading: Geometric Brownian motion and partial differential equations

#### Topics for the first midterm

You are responsible for what we did in class, but the (roughly) corresponding sections are:
• Forward contracts: Chapters 5.1-5.5, 5.7, 5.10-5.12
• Forward rate agreements and swaps: Chapters 4.6-4.7, 7.1, 7.6-7.7
• Futures contracts: Chapters 1.4, 2.1-2.4, 2.11, 5.8
• Options: Chapters 9.1-9.2, 11.2-11.5
• Qualitative properties: Chapter 10.
Last year's first midterm is available here (and also with solutions)

#### Topics for the second midterm

You are responsible for what we did in class. The (roughly) corresponding sections are:
• Binomial trees: 12.1-12.4 and 12.8-12.9
• Lognormal models: 14.1-14.4 (through p. 303 only)
• Risk neutral valuation and BSM: 14.7-14.9 and Ch. 14 appendix
• Dividends and trees: 20.1 through p. 432
• Dividends and BSM: (see the notes)
You aren't responsible for the Central limit argument that we used to obtain lognormal stock prices. But you are responsible for using the lognormal distribution to calculate option prices (eg BSM). You are only responsible for the tree-based model of dividends I called "eg 2", on p. 53.2 of the lecture notes. Not the other tree-based models (ie. egs 1/3/4). You are responsible for BSM with dividends. You will be given a table of the normal distribution for the exam.

Last year's second midterm, with solutions, is available here. Note that the topics weren't identical to the topics for our midterm, since it didn't come at exactly the same point in the term.

### Topics for the final exam

You should bring a calculator and formula sheet (letter sized sheet, double sided) to the final exam. In addition to the material you were responsible for on the first and second midterms, you are responsible for the following topics:
• American options in the binomial model: Chapters 12.5, 20.1
• Greeks. Computation of Delta, and Delta-hedging in the lognormal model: Chapter 18
• Estimating volatility: Chapter 14.4
In other words, no complete markets theory, no Gamma/Theta/etc. beyond simply the definitions, no exotic options, and no GBM.