# Math 339 Fall 2012: Mathematical Finance

## Daily Schedule

# Date Topics (Reading: next columns) 6th, 7th ed. 8th ed. Homework Hull 6th, 7th ed Hull 8th ed
1 W 9/5 Introduction - - - - -
2 F 9/7 Interest rates - - - - -
3 M 9/10 The exponential function - - - - -
4 W 9/12 Returns - - - - -
5 F 9/14 Data analysis I - - HW 1 (due 9/19)(G), HW 2 (due 9/21)(AD) - -
5 M 9/17 Calls Hull Ch 1 Hull Ch 1 - - -
6 W 9/19 Investing, speculating Hull 1.8 (ditto) HW 3 (due 9/26)(G) 1.9, 1.10 (ditto)
7 F 9/21 Puts, calls Hull 1.5 - - - -
8 M 9/24 (con't) - - HW 4 (due 9/28)(G) 1.4, 1.5, 1.7, 1.15, 1.16 (ditto)
9 W 9/26 Simple example of no arbitrage (two banks with different interest rates) - - - - -
- - Hedging with puts Sec. 1.7 (ditto) - - -
10 F 9/28 Pricing a forword sec 5.4; read 5.1--5.3. (ditto) - - -
- - Bachlier diagrams 8.1, 8.2 Suggested reading: all of this chapter 9.1, 9.2 - - -
11 M 10/1 Review for exam (Practice problems and answers on ella) - - - -
12 W 10/3 Spreads (bull, bear, butterfly) 10.2, 10.3 8th: 11.2, 11.3 11.3, 11.4 - - -
13 F 10/5 Exam 1 (on material through 9/24) - - - - -
14 W 10/10 Put-call parity: Proof using portfolios 9.4 10.4 - - -
- - Proof using diagrams - - - - -
15 F 10/12 Binomial trees (an example) 11.1 12.1 HW 5 (due 10/17)(G) 1.27, 1.28, 5.3, 8.1, 8.2, 8.13, 8.15 1.27, 1.28, 5.3, 9.1, 9.2, 9.13, 9.15
16 M 10/15 Binomial trees (general case) 11.1 12.1 HW 6 (due 10/19)(G). Write out all the steps, as in the example at the beginning of this section. 11.1, 11.4 12.1, 12.4.
17 Weds 10/17 Mountain day! - - - - -
18 F 10/19 Preview of Homework 7. Also probabilities, expected value. - - HW 5, 6 are now due 10/22. HW 7 is due 10/24. - -
19 M 10/22 Two-step trees 11.3 12.3 HW 8 (due 10/26) 11.14, 11.17 (see ella announcement) 12.14, 12.17 (ditto)
20 W 10/24 Risk-neutral probabilities 11.2 12.2 - - -
21 F 10/26 Currency forwards 5.10 5.10 HW 9 (handout, also on ella). (due 11/2) - -
- - - - - HW 10 (extra credit, counts for data analysis HWs; see below; due 11/9)) - -
- - Two step trees (general case) 11.3 12.3 - - -
22 M 10/29 Storm--no class - - - - -
23 W 10/31 Random walks - - - - -
- - Quiz 1 (on the method for pricing calls) - - - - -
24 F 11/2 From random walks to geometric Brownian motion (see applets below) 12.1-3 13.1-3 - - -
25 M 11/5 (con't) Practice test posted. - - - - -
26 W 11/7 Ito's lemma 12.5 13.6 - - -
27 F 11/9 Exam 2 (on material through 10/26) - - - - -
28 M 11/12 Black-Scholes PDE 13.5, 13.6 14.5, 14.6 HW 11 (due F 11/16) 12.1, 12.2, 12.8, 12.9 13.1, 13.2, 13.8, 13.9
29 W 11/14 Geometry of the Black-Scholes PDE - - - -
30 F 11/16 Black-scholes formulas 13.8 14.8 HW 12 (due M 11/26). (do the first two problems in two ways: (1) by evaluating the formulas, and (2) check your answers using an applet--see below) 13.13, 13.14 , 13.18. 14.13, 14.14, 14.18
31 M 11/19 Movie: Trillion dollar bet - - - - -
32 M 11/26 Forwards (con't) 5.7 5.7 HW 13 (due 11/30) 5.9 5.9
33 W 11/28 South Hadley stock market - - - - -
34 F 11/30 Using trees to price options 11.7 12.7 - - -
35 M 12/3 Do real stocks follow the abstract model? - - HW 14 (Due 12/7) - -
36 W 12/5 Implied volatility 13.11 14.11 - - -
37 F 12/7 Volatility smiles 18.3 19.3 HW 15 (due end of exam period0) - -
- - Marte Carlo methods 12.3; also 6th ed 17.6. 7th 19.6 13.3; 20.6 HW 16 (extra credit; due end of exam period) - -
38 M 12/10 - - - - - -
- Th 12/13 All homework due by 5pm - - - - -

## Notes

HW 10: (You can do this problem with someone else.) Find an example of the currency forwards: Choose two countries, and a time T when the transaction is carried out. Find the exchange rate now, and the rate at time T. Check whether formula (5.9) in section 5.10 is true. It probably won't be, but an inequality should be true. (If r > f, then you should get F_0 > E_0, and the opposite. (I'm using the notation I used in class.)

HW 12: One applet that looks good can be found at www.math.columbia.edu/~smirnov/options13.html. Also there's the program on the disc that comes with the book.

The statistical applets can be found at www.math.uah.edu/stat/applets/