This page is
www.math.columbia.edu/~bayer/S00/finance.html
Take Home Final: The following take home final is posted in Acrobat .pdf format. Your browser
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This take home final is due at our scheduled
Final Examination, Monday, May 8, 7:10pm-10:00pm, in our regular
classroom. You may also hand in this final in advance.
This course will strike a balance between a general survey of
significant numerical methods any practitioner should know, and a
detailed study of certain numerical methods specific to finance. The
general material will include numerical methods for random number
generation, interpolation, linear algebra, statistics, integral and
differential equations, and linear and integer programming. The
financial material will include the numerical valuation of a variety
of option types, via stochastic differential equations and free
boundary problems.
Prerequisites: Basic principles of numerical analysis.
Familiarity with the basic principles
of partial differential equations, probability and stochastic
processes at the level of Stat W6501 (Stochastic Processes) and of
finance at the level of Math G4071 (Introduction to the Mathematics of
Finance). Some familiarity with computer programming; we will use Mathematica.
Recommended co-requisite: Stat W6505 (Stochastic Methods in
Finance).
Course requirements:
- Programming assignments
in Mathematica. Please submit physical printouts. Please do not
submit assignments by email.
- Final Examination, Monday, May 8, 7:10pm-10:00pm.
Our final will test for an understanding of numerical methods that is
most easily obtained by completing the programming assignments. I will
be flexible in weighting the final, to accommodate students for which
the programming requirement is a particular challenge. All students
are urged, nevertheless, to learn to write simple programs, and to
learn the course material as well as if they had completed all
programming assignments.
Master University Examination Schedule
1999-2000 University Academic Calendar
Office Hours
My office hours for the Spring 2000 semester are
Mondays, 1:30pm-2:30pm
Wednesdays, 4:00pm-5:00pm
and by appointment.
Required Texts:
- William T. Shaw,
Modelling Financial Derivatives with Mathematica,
Cambridge University Press,
ISBN 052159233X.
University bookstore or
Amazon,
Barnes&Noble,
AddALL.
As published, this outstanding text uses Mathematica 3. See
http://www.mathsource.com/Content/WhatsNew/0209-023
for Chapter 1 (available online) and updates to the text, including code for use with
Mathematica 4.
The author
has been very responsive to our adoption of this text, and invites students to
email him with questions and comments. Please don't abuse this priviledge, and try to
make your queries useful to him as author.
-
William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery,
Numerical Recipes in C : The Art of Scientific Computing (2nd Edition),
Cambridge University Press,
1993,
ISBN 0521431085.
University bookstore or
Amazon,
Barnes&Noble,
AddALL.
This book and the accompanying C code is also available online as
Numerical Recipes in C, via the
Numerical Recipes Home Page.
Other texts of interest:
-
Option Pricing: Mathematical Models and Computation,
Paul Wilmott, Jeff Dewynne, and Sam Howison,
Oxford Financial Press, 1993,
ISBN 0952208202.
Amazon,
Barnes&Noble,
Borders.
This text can be ordered directly from the publisher
(phone/fax +44 1249 659697) for £85 ($140),
including delivery by first class/air mail.
Publisher order forms: zipped Word document,
pdf format.
(Amazon.com)
Class Schedule:
Wednesday, January 19
Shaw Introduction. Numerical solution to the heat equation.
Monday, January 24
(Guest lecturer:
Sorin Popescu)
Recipes Chapter 7: Random numbers
Wednesday, January 26
Recipes Chapter 7: Random numbers (continued)
Monday, January 31
Shaw Chapter 4: Mathematical preliminaries
Wednesday, February 2
Shaw Chapter 4: Mathematical preliminaries (continued)
Monday, February 7
Wednesday, February 9
Monday, February 14
Wednesday, February 16
Monday, February 21
Wednesday, February 23
Monday, February 28
Wednesday, March 1
Monday, March 6
Wednesday, March 8
Monday, March 13
Wednesday, March 15
Monday, March 20
Wednesday, March 22
Monday, March 27
Wednesday, March 29
Monday, April 3
Wednesday, April 5
Monday, April 10
Wednesday, April 12
Monday, April 17
Wednesday, April 19
Monday, April 24
Wednesday, April 26
Monday, May 1
Monday, May 8
Final Exam, 7:10pm-10:00pm