## Math 456 Topics in Financial Mathematics

### NEWS

• No news is good news.

### 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.
• 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.
• 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.

### 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 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 978-0-387-31607-9 or 978-0-387-25898-0 or 978-1-4419-2073-7.

Homework assignments:
 HW #1, due Friday, September 25 HW #2, due Friday, October 9 HW #3, due Friday, October 23 HW #4, due Friday, November 13 HW #5, due Monday, November 30 HW #6, due Friday, December 18
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 take-home midterm examination due on Friday, October 30th. The cumulative take-home 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: Letter grade at least: 90% 80% 70% 50% 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 3:30-5pm Central Time, or by appointment.
You are also welcome to attend my other class office hours, MWF 10:30am-Noon 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.