MTH 238, Fall 1999
Topics in Applied Mathematics: Mathematics of Finance
MWF 10:30 - 11:20, 205 Physics
Greg Lawler, 128B Physics

Office Hours: Mondays and Thursdays, 1:30 - 3:00 and by appointment

Text

Baxter and Rennie, Financial Calculus

Topics

This course is an introduction to the advanced mathematics of finance, in particular stochastic calculus. The course will be roughly divided in three parts. First, we will consider pricing in discrete models and show how the assumption of no arbitrage leads to a unique pricing of financial instruments. Next we will consider continuous models. This will require studying the mathematics of continuous processes (Brownian motion and stochastic calculus) and then using this mathematics to price options. Finally, we will study a number of examples of how these techniques can be used on particular models. This last part will include presentations by students in the class. Prerequisites are Math 135 (Probability) or the equivalent.

Notes

As part of the requirements for the course, students (on a rotating basis) will be required to prepare a clean copy (with necessary corrections) of the lecture notes. These notes will be put on reserve in the Math-Physics Library. I will give the schedule of who is responsible for which day --- students can switch their assignments by mutual agreement but they must inform me. Check here for the schedule of note takers.

Homework

There will be weekly homework assignments due on Fridays. The assignment for a particular week will be on material covered by Monday, so it is recommended that you do the assignment by Wednesday and then use Wednesday and Thursdays to ask questions. Late assignments will not be accepted. Some assignments will require simple computer programming. In class we will discuss how to use MATLAB to do some of these assignments. However, students are free to use any computer language or package that they wish to do these assignments. Here are the problems sets in PDF format.
Problem Set 1 (due September 10)
Problem Set 2 (due September 17)
Problem Set 3 (due September 24)
Problem Set 4 (due October 1)
Problem Set 5 (due October 8)
Problem Set 6 (due October 29)
Problem Set 7 (due November 12)
Problem Set 8 (due November 19)
Problem Set 9 (due December 8) (Corrected version posted December 2).

Special Notes

Here are the special notes for the Monday, November 15 class.

Here is a link to some notes on mathematical finance.

Exams

There will be an in-class midterm examination on Friday, October 15. There will be a take-home final examination.

Final Problem Set

Here is a copy of the final problem set. It is due by noon, Saturday, December 18. If by any chance, there are corrections or clarifications on the problems, they will be posted here.

Clarification on Problem 5: It might be true that some of the simulations go to infinity before time 1. If there is a realization that reaches infinity before time 1, then the estimate of the expected value of X_1 is infinity.

Correction to Problem 1f: The word "purchase" should be changed to "sell". American puts give the option to sell and not to purchase.

Correction to Problem 1: In a few places in the opening paragraph S_k is written where Y_k should be written, i.e., in the sentence that starts "Y_k acts differently..." all of the S_k's should become Y_k.

Correction to Problem 5: The SDE should start dX_t rather than X_t.

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Last modified: 11 December 99