Math 4560 and Math 5056
Topics in Financial Mathematics
Fall, 2026
Prof. M. Victor Wickerhauser
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NEWS
- Solutions to HW 1 are now posted here and
on Canvas.
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QUICK LINKS
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Download LibreOffice (for
Windows or MacOS X or Linux on PCs) via this link.
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Download Octave (for
Windows or MacOS X or Linux on PCs) via this link.
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Download Macsyma (for
Windows PCs and various other computers) via this link.
- VIX formula from the CBOE.
- Succinct
list of formulas used in the Black-Scholes options pricing model.
- Article on the Black-Scholes equation for pricing
European Call options.
- Article on Computational
Finance Careers from
Prof. Steven E. Shreve of Carnegie Mellon University.
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Chapter 2 from Peter Richken on Futures and
Forwards and when their prices differ. See p.8, Property 4, for a
concise result.
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"Numerics of Implied Binomial Trees" article by
W.Haerdle and A.Mysickova.
- Links to financial data, courtesy of Mathematics Librarian Eliot Boden:
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EXAMPLE PROGRAMS
Extensions: ".m" is for Octave, ".mac" is for Macsyma, ".odg" is for
LibreOffice Draw, ".ods" is for LibreOffice Calc, ".xls" is for Excel.
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AD.m,
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ADnrt.m,
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bisectEG.m,
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bisection.m,
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BS.m,
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BS.mac,
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BSG.m,
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CRReurAD.m,
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CRReur.m,
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CRRa.m,
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CRRaro.m,
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CRRaroAD.m,
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CRRbin.m,
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CRRboo.m,
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CRRcc.m,
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CRRcho.m,
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CRRcp.m,
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CRRD.m,
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CRRDaeC.m,
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CRRDaeP.m,
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CRRflg.m,
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CRRfltAD.m,
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CRRflt.m,
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CRRfws.m,
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CRRgro.m,
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CRRladC.m,
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CRRladP.m,
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CRRlb.m,
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CRRlbAD.m,
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CRRmargin.m,
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CRRmDaeC.m,
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CRRmDaeP.m,
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CRRmD.m,
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CRRparams.m,
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CRRpuoC.m,
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CRRruoC.m,
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CRRuiC.m,
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CRRuoC.m,
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CRR.ods,
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CRR-1-step.ods,
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CRR-1-step.xls,
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DGS3MO.ods,
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FwdFut.m,
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GLPK.m,
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IBT123J.m,
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IBT123.m,
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MarFut.m,
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NJfromM.m,
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NRTCRR.m,
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NRTinject.m,
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NRTmax.m,
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NRTmin.m,
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NRTpsums.m,
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PathAD.m,
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PathBal.m,
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PathPr.m,
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PrNeg.m,
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RiskNeut.m,
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StreeCRR.m,
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ZCB.m,
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ZT.m,
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VIDEOS
LECTURE EXAMPLES
- ExampleRS.txt Octave
inputs for 10/15/2025 class.
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CallPut.odg, LibreOffice Draw commands
to plot payoffs for Call and Put options.
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weighted-options.txt, commands
to perform weighted generalized least-squares regression on an
options chain of BAC Call options, as begun in lecture on 9/25/2024.
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Syllabus
Description. This course is an introduction to the principles and methods of financial
mathematics, with a focus on discrete-time stochastic models. Topics
include no-arbitrage pricing of financial derivatives, risk-neutral
probability measures, the Cox-Ross-Rubenstein and
Black-Scholes-Merton options pricing models, and implied volatility.
Prerequisites. Math 2130 (formerly 233) Multivariable
Calculus, Math 3010 (formerly 310) Foundations for Higher
Mathematics, and Math 3200 (Introduction to Statistics), or
permission of the instructor. These are the same for both graduates
and undergraduates.
Modality. Classes meet in person for lectures on Mondays, Wednesdays and Fridays, 1:00 pm
to 1:50 pm, in Simon Hall, room 23.
Learning objectives. The lectures will follow my book
Introducing Financial Mathematics: Theory, Binomial
Models, and Applications (2022), ISBN 9781032359854.
Students will be expected to read approximately one chapter and complete the
assigned homework every two weeks.
Homework assignments:
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HW #1, due Friday, September 11th.
(Solutions)
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HW #2, due Friday, September 25th.
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HW #3, due Friday, October 16th.
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HW #4, due Friday, October 30th.
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HW #5, due Friday, November 13th.
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HW #6, due Friday, December 4th.
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Solutions are due by 11pm on the due date. Late homework
will not be accepted.
Homework should be submitted electronically using GradeScope, accessed
from the Canvas website for this course using the "Assignments" menu item.
Final Project. Instead of a midterm or final examination,
students will be required to apply concepts and algorithms from this
course to complete a Final Project Report using software from the course
and data found online. The project must be submitted electronically by
Wednesday, December 16th, 2026, at 11pm. The report should be no more
than 10 pages long.
Prepare an optional one-page Outline by
December 4th, if you wish me to comment on your choices. This should
also be submitted electronically.
Grading. One grade will be assigned for homework (with the lowest
HW score dropped) and one for the final project. These
two will contribute as follows to the course grade: HW 70%, FP 30%.
Letter grades, computed from the course score,
will be at least the following:
| Course score at least: | 90% | 80% | 70% | 50% |
|---|
Letter grade at least: | A | B | C | D |
Students taking the Pass/No Pass option (formerly Cr/NCr or P/F) will
need a grade of D or better to pass. Students auditing the course
will need to show evidence of attending or viewing at least 36 of the
lectures in order to receive a successful audit grade.
Graduate Student Requirements
Students enrolled in the Math 5056 graduate-credit version of this course are
expected to complete work at a level above that required of undergraduate
students, to reflect the greater depth, independence, and
mathematical maturity expected of graduate students.
In particular, letter grades will be computed as follows:
| Course score at least: | 93% | 85% | 77% | 70% |
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Letter grade at least: | A | B | C | D |
Graduate students taking the Pass/No Pass option (formerly Cr/NCr or P/F) will need a
grade of C or better to pass.
Office Hours. MWF 3:00-4:30pm, in my
office in Cupples I, room 105a, or by
appointment.
Questions? Return to
M. Victor Wickerhauser's home page for contact information.