Math 456 Topics in Financial Mathematics

NEWS

• Final Exam is now available.
• HW 6 solutions are now available.
• Octave code IncompleteMarkets.txt to compute a Call option price in an incomplete market, following the example in Appendix B.2 of the textbook.
• HW 6 is now due at midnight on Sunday, Dec. 20th, 2020.

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.

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 (Solutions to HW 1) HW #2, due Monday, October 12th (Solutions to HW 2) HW #3, due Friday, October 23 (Solutions to HW 3) HW #4, due Friday, November 13 (Solutions to HW 4) HW #5, due Monday, November 30 (Solutions to HW 5) (ch10ex1010.ods) (ch10ex1012.ods) (ch10ex1013.ods) (binomialprice.ods) HW #6, due Sunday, December 20 (Solutions to HW 6)
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 take-home midterm examination due on Tuesday, November 3rd, 2020. 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.