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 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 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 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.

Homework assignments:
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 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%, 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:ABCD

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.