Mathematics 16:642:622 Mathematics Finance II

Schedule

The course is offered during the Spring semester.

• Class meeting dates: Please visit the University's academic calendar.
• Schedule and Instructor: Please visit the University's schedule of classes for the instructor, time, and room.
• Instructor and Teaching Assistant Office Hours: Please visit the Mathematical Finance program's office hour schedule.

Note: Please avoid stopping by the course assistant or instructor offices outside of their posted hours without an appointment. You are welcome to alert the instructor if you believe an assignment contains a typographical error, but the course assistants and instructor will rarely answer homework questions by email, except for students who are working full-time off campus and are unable to attend any scheduled office hour. We recommend emailing the instructor or teaching assistant in advance to alert them to your visit, as schedules can sometimes change unexpectedly.

Course Abstract

This course continues the development of the mathematical theory of derivative security pricing begun in Mathematics 16:642:621 and, in addition, focuses on applications to financial models. Topics covered include exotic options (such as barrier, lookback, and Asian options), stopping times, American-style (early exercise) options, McKean's formula for the perpetual American put, change of numéraire and risk-neutral measure, interest rate models, bonds and options on bonds, term-structure models (Heath-Jarrow-Morton model, forward LIBOR model, swap market model), Black's formulae for caps and swaptions. The course ends with an introduction to jump models, including compound Poisson, jump diffusion, and Lévy processes, stochastic calculus and change of measure for jump processes, and option pricing with jump processes.

Pre-requisites and Co-requisites

Math 16:642:621 (Mathematical Finance I).

Required Textbooks

Stephen E. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer Verlag, 2004, ISBN 0-387-40101-8. (Text errata available from author's web site.)

Note: The textbook may be purchased either new or used at significant discounts to the list price from online sellers such as Amazon, Buy, Half, and others found through Google.

Sakai

All course content – lecture notes, homework assignments and solutions, exam solutions, supplementary articles, and computer programs – are posted on Sakai and available to registered students.

Grading

Class attendance 5%, homework 25%, midterm exam 30%, and final exam 40%. Exams are in-class and closed-book.

Class Policies

• Class attendance: Attendance is taken every week and students will be dropped from the course for missing an excessive number of class periods. Students can be absent for one week (two periods) without an excuse. Additional absences must be excused in writing. Unexcused absences will negatively impact course grade.
• Homework: Assignments may be submitted at the beginning of class each week only – assignments left in mailboxes, under office doors, given to departmental staff, emailed, faxed, or mailed are not accepted. No late homework is accepted, for any reason – instead, the two (2) lowest scores are dropped. Students may work together on assignments provided their submissions represent fair individual efforts. Assignments must be legible, stapled (no paper clips or loose sheets), and use US letter-size paper.
• Exam attendance: Make-up exams are not permitted. In a genuine emergency, such as a documented medical condition, students are expected to contact the instructor in advance or as soon as possible after the event.
• Incomplete grades: Incomplete grades are not given. Students who do not have adequate preparation or time to complete assignments or study for exams during the semester should not take the course.
• Academic integrity: Students are expected to adhere to the academic integrity code.
• Work-study balance: If you work part or full time, please read our guidelines for balancing work and study.
• Withdrawal dates: You are responsible for being aware of all deadlines, including those for course refunds or withdrawals. Please contact the Registrar if you are in any doubt regarding drop or refund deadlines.

Weekly Lecturing Agenda and Readings

This page will record the topics we cover in each week, reading assignments, and additional information as needed. Reading material from the texts on the reserve list is strongly suggested, but not absolutely necessary. Reading material from the class text and handouts is required. Students should study the reading assignments before class.

Library Reserves

All textbooks referenced on this page should be on reserve in the Hill Center Mathematical Sciences Library (1st floor). Please contact the instructor if reserve copies are insufficient or unavailable.

Additional Textbooks

Class lectures will draw on material from the following texts and current research articles. Please see the Rutgers Mathematical Finance Reference Texts blog for additional textbooks.

T. Björk, Arbitrage Theory in Continuous Time, Oxford, 2004
R. Cont and P. Tankov, Financial Modeling with Jump Processes, Wiley, 2004
D. Brigo and F. Mercurio, Interest Rate Models - Theory and Practice, with Smile, Inflation, and Credit, 2nd Edition, Springer 2006
J-P. Fouque and G. Papanicolaou and K. R. Sircar, Derivatives in financial markets with stochastic volatility, Cambridge, 2000
J. Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley, 2006
J. C. Hull, Options, Futures, and other Derivatives, 6th Edition, Prentice Hall, 2006
M. S. Joshi, The Concepts and Practice of Mathematical Finance, Cambridge, 2003
I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer, 1997
A. Lipton, Mathematical methods for foreign exchange: a financial engineer's approach, World Scientific, 2001
P. Wilmott, Paul Wilmott on Quantitative Finance, 2nd edition, 3 volume set, Wiley, 2006

Software

Depending on the application, Excel/VBA or MATLAB may be used in the course. Please visit the Quantitative Finance Software blog for a guide to platforms, installation guides, and sample code.

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