Math 456 Topics in Financial Mathematics
Prof. M. Victor Wickerhauser

NEWS
 Final Exam is now available.
 HW 6 solutions are now available.
 Octave code
IncompleteMarkets.txt to
compute a Call option price in an incomplete market, following the
example in Appendix B.2 of the textbook.
 HW 6 is now due at midnight on Sunday, Dec. 20th, 2020.

QUICK LINKS

EXAMPLE PROGRAMS
 LibreOffice Draw commands to plot payoffs for Call and Put options.
 Macsyma code to solve for H0,H1 from
system Eq.2.3 on p.15 in our textbook.
 Octave commands to perform weighted
linear regression for Ex.2.46.
 LibreOffice
spreadsheet binomialprice.ods for
multiperiod binomial model pricing of a dividendless stock and its
European style options.
 LibreOffice spreadsheet jamsh.ods to compute
ArrowDebreu securities prices by Jamshidian's forward induction.
 Octave code binaryCallPut.m for multiperiod
binomial model pricing of binary options.
 Octave code americanCallPut.m for multiperiod
binomial model pricing of American style options.
 Octave code europeanCallPut.m for multiperiod
binomial model pricing of European style options.
 Octave code fwdstartCallPut.m for multiperiod
binomial model pricing of forward start options.
 Octave code compoundCall.m for multiperiod
binomial model pricing of compound call options.
 Octave code chooserOption.m for multiperiod
binomial model pricing of chooser, or "As You Like It" options.
 Octave code binomialTree.m for multiperiod
binomial model pricing of a risky asset.
 Macsyma code to find upstate and downstate interest rates using
the Ho and Lee and Black, Derman, and Toy methods: hlbdt.txt.
 LibreOffice spreadsheet BlackScholes.ods to
price European Call and Put options and compute Greeks by the
Black and Scholes method.
 Octave function BlackScholes.m to
price European Call and Put options by the Black and Scholes method.
 Octave example code HullWhite.txt to
price average rate options by the Hull and White method.
 Octave function asianCallPut.m to
price Asian options by the nonrecombining tree method.
 Octave example code aro.txt for average
rate options.
 LibreOffice spreadsheet ch5eg51.ods
for pricing hedge ratios, following Example 5.1 on p.83 of the text.
 LibreOffice spreadsheet ch6eg63.ods
for pricing futures and forward contracts, following Example 6.3 on
p.92 of the text.
 LibreOffice spreadsheet ch6eg64.ods
for pricing futures and margin accounts, following Example 6.4 on
p.93 of the text.
 LibreOffice spreadsheet ch6eg64x.ods
for pricing futures and margin accounts and opportunity cost,
extending Example 6.4 on p.93 of the text.
 LibreOffice spreadsheets for Chapter 10 dividend
examples 10.3, 10.7,
and 10.8.
 Octave function bisection.m to
solve for p in f(p)=y by the bisection method.
 Octave function ImpliedTree123.m to
find a binomial tree to match market Call prices by the van der
Hoek "One, Two, Three" method.
 Spreadsheet ch12eg2.ods to
find an implied binomial tree, implementing Example 12.2, p.156,
of the textbook.
 Octave code
IncompleteMarkets.txt to
compute a Call option price in an incomplete market, following the
example in Appendix B.2 of the textbook.

VIDEOS

Syllabus
Topics. This course is an introduction to the principles and
methods of financial mathematics, with a focus on discretetime
stochastic models. Topics include noarbitrage pricing of financial
derivatives, riskneutral probability measures, the
CoxRossRubenstein and BlackScholesMerton options pricing models,
and implied volatility.
Prerequisites. Math 233 and Math 3200 or permission of 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 the book Binomial
Models In Finance(2006) by John
van der Hoek and Robert J. Elliott, ISBN 9780387316079 or
9780387258980 or 9781441920737.
Homework assignments:

 HW #1, due Friday, September 25
(Solutions to HW 1)
 HW #2, due Monday, October 12th
(Solutions to HW 2)
 HW #3, due Friday, October 23
(Solutions to HW 3)
 HW #4, due Friday, November 13
(Solutions to HW 4)
 HW #5, due Monday, November 30
(Solutions to HW 5)
(ch10ex1010.ods)
(ch10ex1012.ods)
(ch10ex1013.ods)
(binomialprice.ods)
 HW #6, due Sunday, December 20
(Solutions to HW 6)


Solutions are due by 11:01pm on the due date. Late homework
will not be accepted. The homework will sometimes require writing a
working computer program, which will be judged for correctness and clarity.
Homework should be submitted electronically using CrowdMark.
The homework portion of your grade will be calculated from your 5 best
HW scores.
Tests. There will be one
takehome midterm examination due on
Tuesday, November 3rd, 2020. The
cumulative takehome final examination, which will emphasize
material in the latter part of the course, must be completed on
Crowdmark by January 8th, 2021, at 11:01pm.
Grading. One grade will be assigned for homework (best 5 of
the 6 scores), one for the
midterm examination, and one for the final examination. These
three will contribute as follows to the course grade: HW 40%, Midterm 30%,
Final 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 42 lectures in order to receive a successful audit grade.
Office Hours. On Zoom only, MWF 3:305pm Central Time, or by
appointment.
You are also welcome to attend my other class office
hours, MWF 10:30amNoon Central Time, though the other students will
have priority.
Zoom invitations were sent Wed., Sep 10th by email
to all registered students. Email me if you didn't get one.
Questions? Return to
M. Victor Wickerhauser's home page for contact information.