Math 456
Topics in Financial Mathematics

Prof. M. Victor Wickerhauser

NEWS

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 Arrow-Debreu 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 non-recombining 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 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 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.

Homework assignments:
Solutions are due by 11:01pm on the due date. Late homework will not be accepted. Homework should be submitted electronically using CrowdMark.

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, December 1, 2021, and the project must be submitted to Crowdmark by Wednesday, December 17th, 2021, at 11:01pm.

Grading. One grade will be assigned for homework (best 11 of the 12 scores) 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:ABCD

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 2:30-4pm Central Time (USA), or by appointment.


Questions? Return to M. Victor Wickerhauser's home page for contact information.