Math 456 Topics in Financial Mathematics
Fall, 2019
Prof. M. Victor Wickerhauser

NEWS
 The homework portion of your grade will be calculated from your
5 best scores.
 HW 6 is now due Monday, December 9th at 11:01pm.
 HW 6 is now available.

QUICK LINKS

EXAMPLE PROGRAMS
 Octave function ImpliedTree.m to
find a binomial tree to match market Call prices by the van der
Hoek method.
 Octave function bisection.m to
solve for p in f(p)=y by the bisection method.
 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 binomialprice.ods for
multiperiod binomial model pricing of a dividendless stock and its
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.
 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.
 Macsyma code to find upstate and downstate interest rates using
the Ho and Lee and Black, Derman, and Toy methods: hlbdt.txt.
 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 Draw commands to plot payoffs for Call and Put options.

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 Eads Hall room 103.
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 Monday, September 9
(Solutions)
(graphs hw1ex239.pdf,
hw1ex240.pdf,
hw1ex241.pdf,
hw1ex244.pdf)
 HW #2, due Monday, September 23
(Solutions)
 HW #3, due Monday, October 7
(Solutions)
(ch5eg51.ods)
(ch6eg63.ods)
 HW #4, due Monday, November 4
(Solutions)
 HW #5, due Monday, November 18
(Solutions)
(ch10ex1010.ods)
(ch10ex1012.ods)
(ch10ex1013.ods)
 HW #6, due Monday, December 9th


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.
Tests. There will be one midterm examination on Wednesday,
October 23rd, 2019, in class. The cumulative takehome final
examination, which will emphasize
material in the latter part of the course, is due by 11:01PM on
Sunday, December 15th, 2019. It must be submitted on Crowdmark.
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%  60% 
Letter grade at least:  A  B  C  D 
Students taking the Cr/NCr or P/F options will need a grade of
C+ or better to pass.
Students auditing the course will need to sign in to at least 40 of
the 45 lectures in order to receive a succesful audit grade.
Office Hours. See the instructor in Cupples I, room 105a, on
Wednesdays or Fridays from 4:00 pm to 5:00 pm, or by appointment.
Questions? Return to
M. Victor Wickerhauser's home page for contact information.