Math 339 Fall 2008: Mathematical Finance

Daily Schedule

# Date Topics References Homework
1 F 9/5 Introduction - Browse in the chapters in S&P Guide on money, stocks and options
2 M 9/8 Interest Handout -
3/td> W 9/10 Present and future value HW1, also two problems at the end of above handout. (due 9/12) -
4 F 9/12 A simple example of arbitrage; also downloading data - HW 2
5 M 9/15 A quick trip through probability and statistics Handout HW 3 (due 9/24)
6 W 9/17 Futures; pricing forwards, case when F > S e^{rT} Browse in the last section of [S&P] and [H] 1.3, 1.4, chapters 2 and 3. Pricing forwards: 5.4 For practice, work out case when F < Se^{rt}. Don't look in the book! We will take up this topic again on Monday.
7 F 9/19 A quick trip through probability and statistics (con't) - -
8 M 9/22 Pricing forwards, case when F < S e^{rT} - -
- - Selling short [H] 5.2; [S&P] p. 50 -
- - Introduction to options: calls [H] 1.5; [S&P] p. 142 -
9 W 9/24 [Mountain day] - -
10 F 9/26 Introduction to options (con't): puts, hedgers and speculators [H] 1.6--1.10. -
11 M 9/29 Introduction to options (con't): short calls and puts; Bachlier diagrams [H] 8.1, 8.2 -
12 W 10/1 Bull and bear spreads [H] 10.2 -
- - - Margins (reading assignment [H] p. 27-30 and p. 194) -
13 F 10/3 Analyse stock data using SPSS - HW 4 (due 10/8)
14 M 10/6 Proof that the two common ways of writing e^x are the same -Handout HW 5: Hull p. 16: 1.4, 1.7, 1.9 (When you evaluate the potential gains and losses in problem 1.9, assume that the price of the stock in 3 months is either $40 or $25.), 1.27; p. 201: 8.4 (due 10/10)
15 W 10/8 Random walks [Handout] -
16 F 10/10 Brownian motion [Handout] -
- M 10/13 [Fall break] - -
17 W 10/15 [no class] - -
18 F 10/17 [no class] - -
19 M 10/20 - - HW 6 (due 10/24)
20 W 10/22 One-step binomial trees [H] 11.1 Problem 11.1 p. 261 (this will be part of your next HW assignment)
21 F 10/24 One-step binomial trees, abstract version [H] 11.1 -
22 M 10/27 Risk-neutral valuation [H] 11.2 -
23 W 10/29 Two-step binomial trees [H] 11.3 Exam I handed out.
24 F 10/31 The South Hadley Stock Exchange (SHSE) None; just 40 cents in change, shares of stock in Mount Holyoke, Smith and Amherst Colleges, and blank forms for long/short calls -
25 M 11/3 Put-call parity Hull 9.4 Exam I due.
- - Spreads: The condor (constructed using calls) Hull 10.2 (The condor is not in Hull, but other examples of spreads are.) HW 7: p. 261: 11.1, 11.4 (Do both directly, as on pp. 241--2, and also using risk-neutral probabilities, as in 11.2), 11.5, 11.6 (use risk-neutral probabilities). Also construct a condor using puts. (Do the condor problem on a separate sheet of paper. Put the condor at the top, and line up below it the various puts you need to construct it.) (Due 11/7)
26 W 11/5 Brownian motion and generalized Brownian motion in SDE notation Hull 12.1, 12.2 -
27 F 11/7 Geometric Brownian motion (the model for stock prices) Hull 12.3. -
- - Estimating the parameters in the GBM model from daily data Handout: from random walk to GBM -
28 M 11/10 Binomial trees for American options Hull section 11.5, p. 250 -
- - The Black-Scholes formula Hull section 13.8, p. 295 -
29 W 11/12 Ito's lemma Hull 12.5, and appendix. Handout HW 8: p. 262: 11.17, 11.18, 11.19. Also p. 306: 13.4, 13.13 (Do the last two by hand using the BS formula.) Due 11/17
30 F 11/14 The Black-Scholes-Merton PDE Hull Section 13.6, p. 291 -
31 M 11/17 - - -
32 W 11/19 Video: The trillion dollar bet about Long Term Capital Management (currently on reserve at Library) Hull business snapshot p. 30; the book When Genius Failed; Wikipedia reference -
33 F 11/21 - - -
34 M 11/24 Introduction to Derivagem Handout -
- - Implied volatility; volatility smiles Hull 13.11 (p. 300); 16.3 (p. 379) -
35 M 12/1 The value of a forward contract Hull 5.7 p. 107 -
36 W 12/3 Currency options Hull 5.10 p. 112 -
37 F 12/5 Delta the Greek - -
38 M 12/8 Guest spreaker: Jan Albano, Associate Treasurer: The college's finances - -
39 W 12/10 Testing stocks for GBM (handout) - -
- - The Monte Carlo method for evaluating derivatives (handout) - -
40 F 12/12 Course summary - HW 9: Testing stocks for GBM (Extra credit; due at the end of exam period)
- - - - HW 10 (extra credit): Solve problems 13.4 and 13.13 (Hull) in three ways: (1). Via the BS formula (use Derivagem); (2) Via trees (use Derivagem). Write down the answers for 6, 7, 8, 9 and 10 steps. If possible, print out the ten-step tree (on one sheet of paper) (3) Via the Monte Carlo method. (Due at the end of exam period)