Prof. Wickerhauser's Math 456 class

Math 456
Topics in Financial Mathematics

Prof. M. Victor Wickerhauser

NEWS

HW 3 is now available.
HW 2 is now due Wednesday, Oct 4th.
Solutions to HW 1.

QUICK LINKS

Download LibreOffice (for Windows or MacOS X or Linux on PCs) via this link.
Download Octave (for Windows or MacOS X or Linux on PCs) via this link.
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.
Chapter 2 from Peter Richken on Futures and Forwards and when their prices differ. See p.8, Property 4, for a concise result.
"Numerics of Implied Binomial Trees" article by W.Haerdle and A.Mysickova.

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.

AD.m,
ADnrt.m,
bisectEG.m,
bisection.m,
BS.m,
BS.mac,
BSG.m,
CRReurAD.m,
CRReur.m,
CRRa.m,
CRRaroAD.m,
CRRbin.m,
CRRboo.m,
CRRcc.m,
CRRcho.m,
CRRcp.m,
CRRD.m,
CRRDaeC.m,
CRRDaeP.m,
CRRflg.m,
CRRfltAD.m,
CRRflt.m,
CRRfws.m,
CRRgro.m,
CRRladC.m,
CRRladP.m,
CRRlbAD.m,
CRRmargin.m,
CRRmDaeC.m,
CRRmDaeP.m,
CRRmD.m,
CRRparams.m,
CRRpuoC.m,
CRRruoC.m,
CRRuiC.m,
CRRuoC.m,
CRR.ods,
CRR-1-step.ods,
CRR-1-step.xls,
DGS3MO.ods,
FwdFut.m,
GLPK.m,
IBT123J.m,
IBT123.m,
MarFut.m,
NJfromM.m,
NRTCRR.m,
NRTinject.m,
NRTmax.m,
NRTmin.m,
NRTpsums.m,
PathAD.m,
PathBal.m,
PathPr.m,
PrNeg.m,
RiskNeut.m,
StreeCRR.m,
TNote.m,
ZCB.m,
ZT.m,
LibreOffice Draw commands to plot payoffs for Call and Put options.

VIDEOS

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 Louderman Hall, room 458.

Text. The lectures will follow my book Introducing Financial Mathematics: Theory, Binomial Models, and Applications (2022), ISBN 9781032359854.

Homework assignments:

HW #1, due Monday, September 18th. (Solutions)
HW #2, due Wednesday, October 4th.
HW #3, due Monday, October 23rd.
HW #4, due Monday, November 6th.
HW #5, due Monday, November 20th.
HW #6, due Monday, December 11th.

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.

	HW #1, due Monday, September 18th. (Solutions) HW #2, due Wednesday, October 4th. HW #3, due Monday, October 23rd. HW #4, due Monday, November 6th. HW #5, due Monday, November 20th. HW #6, due Monday, December 11th.

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 using software from the course and data found online. Requirements will be posted by Wednesday, November 29th, 2023, and the project must be submitted electronically by Friday, December 15th, 2023, at 11:01pm.

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%
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.

Math 456 Topics in Financial Mathematics