Math 456
Topics in Financial Mathematics
Prof. M. Victor Wickerhauser
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NEWS
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Today's office hour (Nov 20th) is postponed until 3-4pm.
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HW 5 Solutions 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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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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VIDEOS
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Syllabus
Topics. 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-Rubinstein and Black-Scholes-Merton options pricing models,
and implied volatility.
Prerequisites. Math 233, Math 310, and Math 3200, or
permission of the instructor.
Time. Classes meet Mondays, Wednesdays and Fridays, 1:00 pm
to 1:50 pm, in McDonnell Hall, room 162.
Text. The lectures will follow my book
Introducing Financial Mathematics: Theory, Binomial Models, and Applications (2022), ISBN 9781032359854.
Homework assignments:
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HW #1, due Friday, September 13th.
(Solutions).
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HW #2, due Friday, September 27th.
(Solutions).
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HW #3, due Friday, October 18th.
(Solutions).
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HW #4, due Friday, November 1st.
(Solutions).
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HW #5, due Monday, November 18th.
(Solutions).
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HW #6, due Friday, December 6th.
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Solutions are due by 11:01pm 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. Requirements will be posted by Wednesday,
November 27th, 2024, and the project must be submitted electronically by
Friday, December 13th, 2024, at 11:01pm.
Prepare a one-page Outline by
December 6th, 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
three 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% |
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Letter grade at least: | A | B | C | D |
Students taking the Cr/NCr or P/F options 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.
Office Hours. MWF 2-3pm, namely after each class, in my
office in Cupples I, room 105a, or by
appointment.
Questions? Return to
M. Victor Wickerhauser's home page for contact information.