Topics in Financial Mathematics
Prof. M. Victor Wickerhauser
- 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.
- Octave function ImpliedTree.m to
find a binomial tree to match market Call prices by the van der
- 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 non-recombining tree method.
- Octave example code aro.txt for average
- 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.
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.
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-Rubenstein and Black-Scholes-Merton 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 978-0-387-31607-9 or
978-0-387-25898-0 or 978-1-4419-2073-7.
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.
- HW #1, due Monday, September 9
- HW #2, due Monday, September 23
- HW #3, due Monday, October 7
- HW #4, due Monday, November 4
- HW #5, due Monday, November 18
- HW #6, due Monday, December 9th
Tests. There will be one midterm examination on Wednesday,
October 23rd, 2019, in class. The cumulative take-home 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%,
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.