Mathematics of Finance, Fall 2015

Department of Mathematics,
Courant Institute of Mathematical Sciences,
New York University
Lectures: Monday,, Wednesday 9:30-10:45, WWH 202
TA sessions: Friday, 12:30-1:45, WWH 201


Jonathan Goodman
room 529 Warren Weaver Hall
office hours: 2 to 4 pm Thursdays
          or by appointment

Teaching Assistant


          or by appointment

Course description

Introduction to the mathematics of finance. Topics include: "Bond math" (the yield curve), No arbitrage theory of pricing and hedging options, Risk neutral probability in complete markets without arbitrage, Mean/variance portfolio theory and the efficient frontier, The binomial tree model and the role of volatility, The lognormal model and the Black Scholes formula, Merton's optimal dynamic investment theory and dynamic programming.

This is an advanced undergraduate level class in applied mathematics. It uses the full range of mathematical tools, including theoretical reasoning (proofs), modeling, useful simplifying approximations, and computing. Students will write basic programs in R.


Multi-variable calculus, partial derivatives, multiple integrals, multi-variate chain rule. A good calculus based course on probability, probability densities and expectation integrals, Bayes' rule, independence, conditional and marginal probability, the law of large numbers and the central limit theorem. Linear algebra, vector spaces, solving systems of linear equations.


The final grade will be based on

  • Weekly homework assignments, posted on Wednesday and due on the following Monday.
  • A preliminary 30 minute quiz, Monday, October 5.
  • A midterm exam, whole period, Monday, October 26.
  • A final exam.

Communication and announcements

There is a course page on the NYU Classes site. Look there for important course announcements, in particular corrections to assignments. This site has a class message board that everyone in the class can see. If you have a technical question or comment, please post it there rather than sending an email to the instructor or the TA. That way everyone can see the question (and be grateful someone asked it) as well as the answer. If you think there is something wrong with the lecture notes or an assignment, please post as soon as possible. The instructor and TA will check this site often to post replies. Please feel free to reply to other posts if you have something to contribute, even if it's just more questions. Polite and constructive feedback on the class (particularly helpful negative feedback) also is encouraged. Also welcome are posts intended for other students rather than the instructor or TA. You can check your grades on Blackboard. If you are an NYU student not registered for the class, email the instructor for access. Please email the instructor or TA only for personal matters (schedule an appointment, request to submit an assignment late, etc.).


The assignments will require some lightweight computing in R. Previous experience with R specifically is not needed, but students should have some exposure to programming in R, or C, or C++, Java, Python, Matlab, VBA, Fortran, etc. The R package is available as a free download. Students will learn the R they need, often through provided code templates, as the course progresses.

Academic integrity (cheating)

Please the NYU CAS academic integrity policy. All those rules apply to this class. Unless explicitly stated in writing on the assignment, all homework in this class is individual. Students may not hand in work they have copied from another source. Students are forbidden to allow their homework to be copied for the purpose of cheating. If assignments from different students have similarities that show one was copied from the other, both students will be penalized. This applies to written work and coding.

The instructor (I) will try to create an environment that does not encourage academic integrity violations. I will ensure that the work load is managable by an individual student working independently. I will work with the grader and TA to identify violations. This will minimize the benefit of cheating and ensure that those who don't cheat are not at a disadvantage. I will listen to anyone's thoughts or complaints on this issue. Please let me know if the work load is unmanageable or if you suspect others of cheating.