York University

GS/MATH 6910.03AF, Fall 1999

STOCHASTIC CALCULUS IN FINANCE
Course Outline

Prerequisites:

Calculus and some basic probability. In particular, Measure Theory is not assumed. This course is designed (and required) for the Diploma in Financial Engineering, which can be pursued in conjunction with either an M.A. or an M.B.A.. Other students are also welcome in the course.

Degree credit exclusions:

None. In particular, though there may be some overlap with the Measure Theory and Stochastic Processes courses (see MATH6280.03 and MATH6602.03 in the grad calendar), mathematics or statistics students are encouraged to take the latter as well.

Instructor:

Tom Salisbury

email: salt@yorku.ca
Office: N625 Ross Building
Phone: (416) 736-5250 (via Math Dept.)
(416) 736-2100 extension 33938 (via York switchboard)
Fax: (416) 736-5757

Lectures:

S173 Ross, Wednesdays and Fridays, 10:00 - 11:30

Course Webpage

Office hours:

Monday 10:30-11:20, Friday 12:30-1:20.
If you need to see me outside these hours, you are welcome to drop by my office. If I am able to talk to you then, I will; if not we can arrange another time. Or you can e-mail to arrange an appointment.

Grading:

30% Assignments (three or four)
30% Project
40% Final exam (take-home)

The project will be on a topic you select and clear with me, that must involve stochastic calculus in some way (applying it, explaining some results or ideas, etc.). You'll write it up and give a 20 minute presentation to the class summarizing what you did.

Text:

Stochastic Differential Equations by Oksendal; 5th edition, Springer Verlag 1998.
This book has been ordered, and is available at the bookstore. I'll refer to it frequently. It is a textbook level introduction to stochastic calculus.

Other references:

Financial Calculus by Baxter and Rennie; Cambridge 1996.
This book is also at an introductory level, and focuses more on finance than Oksendal, but does much less stochastic calculus. It has the best textbook level introduction I have seen to the ideas of risk-neutral pricing.
Introduction to Stochastic Integration by Chung and Williams, 2nd edition, Birkhauser 1990.
A nice textbook level introduction to stochastic calculus. More theory than Oksendal but fewer applications.
Reference books for stochastic calculus, doing much more than we'll have time for:
- Brownian Motion and Stochastic Calculus by Karatzas and Shreve, Springer.
- Continuous Martingales and Brownian Motion by Revuz and Yor, Springer.
- Diffusions, Markov Processes, and Martingales, Vol 1,2 by Rogers and Williams, Wiley.