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# York University

## GS/MATH 6910 3.0AF, Fall 2002

# 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, MATH6602.03, or MATH 6604.03 in the
grad calendar),
mathematics or statistics students are encouraged to take the latter as
well.
### Instructor:

Tom Salisbury
- email: salt@yorku.ca
- Office: N522 Ross Building
- Phone: (416) 736-5250 (via Math Dept.)

(416) 736-2100 extension 33901 (via York switchboard)
- Fax: (416) 736-5757

### Lectures:

Tuesdays, 11:30-2:30, in 129 CCB, with the normal 30 minutes of breaks.

Note that since several students have a class immediately beforehand,
we will normally start at 11:40, take a 10 minute break roughly half
way through, and then finish at 2:20.
### Office hours:

My schedule seems to be wildly unstable, so if you have questions
about the course, the best
thing is just to take your chances dropping by my office. Or to phone my
office (or send e-mail to srainey@yorku.ca) to
arrange an appointment.
### Grading:

- 25% Assignments (two)
- 30% Project
- 20% Midterm exam
- 25% Final exam

The midterm exam will last one hour.
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,
...) You must do it in groups of between two and four people. You can form
your own group, or have me form a group for you. You
will write it up (10-15 pages) and give a 15 minute presentation to the
class summarizing the most important points of your report.
### Text:

*Stochastic Calculus and Financial Applications*
by J.M. Steele; Springer Verlag 2001.

This book has been ordered, and is available at the bookstore. I'll refer to
it frequently. It does stochastic calculus, together with a reasonable
amount of the financial and probabilistic background material. It
takes a fairly relaxed approach, focusing on the ideas rather than on putting
in every technical detail.
### Other references:

*Financial Calculus* by Baxter and Rennie; Cambridge 1996.

A nice survey of the ideas behind risk neutral valuation. Not much
detail about stochastic calculus though.
*Introduction to Stochastic Calculus Applied to Finance*
by Lamberton and Lapeyre, Chapman and Hall 1996.

A readable survey of
stochastic calculus and its applications in finance.
- Textbook-level treatments of stochastic calculus:
*Introduction to Stochastic Integration* by Chung and Williams, 2nd
edition, Birkhauser 1990.

A nice introduction to the theoretical side of stochastic calculus.
*Stochastic Differential Equations* by Oksendal, 5th edition,
Springer Verlag 1998.

More applications, mostly not to finance though.

- 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.

- Reference books for mathematical finance:
*Martingale methods in financial modelling* by Musiela
and Rutkowski, Springer 1998.
*Methods of mathematical finance* by Karatzas and Shreve,
Springer 1998.