Math 225 - Introduction to Financial Mathematics

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This is the home page for Math 225 for fall, 2004.

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12/8/04, 2pm - Here are the answers to homework 9. Also posted below: the second handout on mean-variance optimization (with a bit of the Capital Asset Pricing Model).

11/28/04 - Here are the answers to exam 2. Perhaps the exam was long and hard, but for the most part you did very well.

11/21/04 - Homework 9 is posted below, and so is a 5-page handout planned for tomorrow. Both are Word documents.

11/18/04 - Alert! In problem 2 of the exam, you're told that S(2) represents the price four years from now. Of course, it represents the price TWO years from now. Sorry. Also, here is a normal distribution table (PHI(z)) if you haven't found one already.

11/17/04 - Also below - solutions 8, exam cover sheet (with references), and a handout on option valuation (revised from another occasion, but maybe better than nothing).

11/16/04 - Finally posted below are homeworks 7 and 8 (as revised), and the answers for homeworks 6, 7, and 8. Also the "what's on the exam" sheet for exam 2. More coming. The exam will be ready to hand out tomorrow (Wednesday 11/17) for return by class time Monday (11/22).

10/21/04 - Various documents are posted below, including homework 6, homework 5 answers, the 10/18 handout on the Black Scholes formula, and the Excel spreadsheet used in class 10/20.

Here's a rough schedule for the coming weeks:

(A) Black-Scholes without the risk neutrality assumption

Week 8 (Oct. 25-29) -- Pricing by arbitrage. Text, chapter 5. The two-branch model, binomial tree models (text, chapter 6.2), put-call parity.

Week 9 (Nov. 1-5) -- The "arbitrage theorem" from chapter 6. "Risk-neutral prices." Pricing by replication.

Week 10 (Nov. 8-12) -- Finishing the Black-Scholes model. Other applications of the binomial tree model with risk-neutral pricing.

(B) Portfolio optimization

Weeks 11-14: Portfolio optimization and other fun stuff.

10/5/04 - Homework 5 is posted (WORD, 1 page). Answers, too.

10/2/04 - Here are solutions to the exam (WORD, 4 pages). Most people did very well. (There is no longer any need to be discreet about the contents of the exam.)

9/29/04 - Here's the what's-on-the-exam sheet (WORD, 1 page). And the cover sheet of the exam (as taped to the envelope, with formulas) (WORD, 1 page). You may use this cover sheet as a reference during the exam. The posted version includes a correction: D(t)=exp(+rt) in place of D(t)=exp(-rt) (although stripped of context, it's hard to say whether either version is "correct").

9/28/04 - Here's a solution set for homework 4. (You might still get it back tomorrow.) It's way too wordy, but if you're feeling vague about some of the problems then maybe that's what you want. (WORD document, 5 pages.)

9/22/04 - Don't forget Art Benjamin's colloquium talk (ways to count things using determinants) Monday 9/27 at 4pm in Park 328 (refereshments earlier), or his math-and-magic demo at 8pm in the Physics Lecture Hall.

EXAM: Self-scheduled, to you on Wednesday, Sept. 29, for return at start of class Friday, Oct. 1. Covers interest (including, but not limited to, text ch. 4), probability (text ch. 1 and 2.1-2.2), modeling stock prices. More details later.

Homework 4 is posted below. It's as follows: Read ch. 1 and 2.1-2.2; turn in ch.1 ## 2,4,7,8,9b,11,12,19 and (subject to change) ch.2 ## 1,3; and read chapter 2 problem 9.

9/21/04 - Homework 3 answers are below (WORD version only).

9/15/04 - Homework 3 and the answers to homework 2 are below. Also, the "download" instructions and the spreadsheet from class.

9/8/04 - Homework 2 and the answers to homework 1 are below.

9/7/04 - This web page is up. The texts are at the bookstore. This section of the page will be managed in a rough weblog style: I'll feel free to edit the most transient remarks, and other notes will stay on the page in reverse chronological order. Below is a list of course documents (both serious and trivial), also in reverse chronological order.

**Course documents:**

225exam2solutions.doc - Exam 2 answers, 11/29/04 (WORD, 7 pages)

MeanVariance.doc - handout on mean-variance optimization, 11/22/04 (WORD, 5 pages)

MeanVariance2.doc - second handout on mean-variance optimization - followup on Capital Asset Pricing Model, 12/6/04 (WORD, 3 pages)

homework9answers.doc - 12/8/04 (WORD, 4 pages).

homework9.doc - 11/22/04, due 12/1/04 (WORD, 1 page)

FinanceNotes2004.doc - rough notes on option valuation, 11/17/04 (WORD, 10 pages).

225exam2cover.doc - cover sheet for Exam 2, with reference material (WORD, 1 page).

preexam2.doc - "What's on the exam" #2, 11/15/04 (WORD, 2 pages).

homework8answers.doc - 11/17/04 (WORD, 4 pages).

homework8.doc - as revised 11/12/04, due 11/17/04 (WORD only; 2 pages).

homework7answers.doc - 11/16/04 (WORD, 2 pages).

homework7.doc - 10/29/04, due 11/1/04 (WORD only; 1 page).

homework6answers.doc - 11/16/04 (WORD, 2 pages).

BlackScholes.xls - Excel implementation of Black-Scholes call option formula, from class 10/20/04. *(Link corrected 10/22 10:30pm)*

notesOct18.doc - handout on derivation of Black-Scholes assuming risk-neutrality, from class 10/18/04.

homework6.doc - 10/20/04, due 10/25/04 (WORD only; 2 pages).

homework5answers.doc - 10/20/04 (WORD, 4 pages).

homework5.doc - 10/6/04, due 10/20/04 (WORD only; 1 page).

225exam1solutions.doc - Exam 1, with solutions and point values added 10/2/04 (WORD, 4 pages).

225exam1cover.doc - Cover sheet for exam 1, 9/29/04 (corrected 9/30) (WORD, 1 page)

preexam1.doc - "What's on the exam", 9/24/04 (WORD, 1 page)

homework4answers.doc - homework 4 answers, 9/28/04. (WORD format only, 5 pages)

homework4.html - homework 4, 9/22/04, due 9/27/04

downloading.doc - instructions for downloading prices for one company, 9/13/04 (Word document, 1 page)

mdt1.xls - spreadsheet from class (as of end of class 9/15/04)

homework3answers.doc - homework 3 answers, 9/21/04. (WORD format only, 2 pages)

homework3.html - homework 3, 9/8/04, due 9/13/04

homework3.doc - same, Word version (1 page, I think)

homework2answers.html - 9/8/04

homework2.html - homework 2, 9/8/04, due 9/13/04

dcf1.xls - spreadsheet used in class 9/6/04

Interest3.doc - handout on interest rates, 9/24/04 (Word document, 6 pages, replacing earlier handout of 9/3/04}

homework1answers.html - 9/8/04

homework1.html - homework 1, 9/1/04, due 9/8/04

FactsFromCalculus.doc - items to remember from calculus, 8/30/04 (Word document, 1 page)

syllabus225.html - Course description, contact information, 8/30/04

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