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Economics 765

This page is for the course entitled Models for Financial Economics. The course is offered in the spring, in the months of May and June.

Class Notices:

The class outline for 2020 is here as a PDF file, and here in HTML. The information it contains is also given below.

We will meet virtually, via Zoom, on Tuesdays and Thursday, from 10.00 until 13.00 Montreal time. I know that some people, including me, are not in that time zone, and so, if you are elsewhere, be sure to know what the time difference is. Judging by the first class, though, everyone is aware of this - no flat earthers!

I received word today (June 9) that you may now complete the Mercury course evaluation, at this site. I need a minimum of five (5) responses for the results to be made available.

The course is directed to students who wish to learn the mathematical techniques used in modern finance theory. The course will also include the basic theory of asset pricing, in particular, the pricing of derivative assets, such as options. If time permits, more elaborate models will also be discussed. The introductory material starts with measure theory, a topic not always treated in courses of mathematics for economists. Measure theory is however a necessary prerequisite for the sort of probability theory needed for financial applications. In particular, we will treat stochastic processes in continuous time, of which the simplest example is Brownian motion.

A brief list of the foundational topics we will treat is as follows.

On the more applied side, we will consider

We will follow the two-volume set entitled Stochastic Calculus for Finance, by Steven Shreve, in the Springer Finance series. The first volume contains no sophisticated mathematics, but allows readers to develop valuable intuition by a detailed treatment of the so-called binomial model, the simplest of all models of derivative pricing. We will make use of many of the examples in that volume. The second volume is where most of the material for the course is to be found. It combines mathematical developments with some quite sophisticated financial models.

I have from time to time drawn attention to misprints and errors in Volume 2 of Shreve's book. I have located Shreve's own list of errata, which is in fact a lot more comprehensive than my own observations would have led me to think. Here is the PDF file containing these errata .

Log of material covered



Here is the link to the notes on various topics prepared to complement or explain the material in Shreve's book.


This link is to the first assignment. It is due on Thursday May 21.

This link is to the second assignment. It is due on Thursday May 28.

This link is to the third assignment. It is due on Thursday June 4.

This link is to the fourth assignment. It is due on Thursday June 11.

This link is to the fifth assignment. It is due on Thursday June 18.

Final Exam:

The Final Exam is now available. It should be completed and returned to me by Thursday June 25 at the latest.

Other links:

By chance I came across an article (in French) written by a Parisian probabilist on the "History of Martingales". It gives a fairly complete account of the numerous senses of the word "martingale", and explains the best modern theories as to why the word means what it does in Probability theory. The article is well written and amusing, as well as being scholarly. It can be found here as a PDF file.

The article found by following this link, by Jarrow and Protter, gives a history of the development of stochastic calculus and its application to mathematical finance. It includes the sad tale of Doeblin, and explains why a Frenchman had a German name.

The picture I found of Catherine Doléans-Dade is contained in a set of slides prepared by B. Hajek from Urbana-Champaign. It contains interesting biographical material on this excellent female mathematician, and some background on her work.

In order to encourage the use of the Linux operating system, here is a link to an article by James MacKinnon, in which he gives valuable information about what software is appropriate for the various tasks econometricians wish to undertake.

To send me email, click here or write directly to Russell.Davidson@mcgill.ca.

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URL: https://russell-davidson.arts.mcgill.ca/e765/