AMS 511 - Foundations of Quantitative Finance

Online - Fall 2023

Prof. Robert J. Frey, Instructor




Course Lecture:

    Wednesday, 02:40 PM - 05:30 PM

    Online via Zoom


Office Hours:

    Online via Zoom

Jason Bohne, Teaching Assistant


Office Hours:

    Online via Zoom

Due to the ongoing COVID pandemic, this course will be held online. This is a new experience for many students and instructors, so bear with us as we endeavor to make things work as smoothly as possible. Constructive criticisms and suggestions are encouraged. Don't be afraid to speak up if you have any problems or ideas!


For the latest COVID guidance see: https://www.stonybrook.edu/commcms/strongertogether/latest.php


  • This page is updated regularly with new information and downloads. Be sure to reload an open page to ensure that you have the most current version.


  • Be sure to check the Announcements and Updates section on my home page for information about schedule changes, class cancellations, up coming seminars and events, and other important news.


On This Page



Course Overview


Introduction to capital markets and modern portfolio theory, including the organization and operation of securities markets, the Efficient Market Hypothesis and its implications, the Capital Asset Pricing Model, the Arbitrage Pricing Theory and more general factor models. Common stocks and their valuation, statistical analysis, and portfolio selection in a single-period, mean-variance context will be explored along with its solution as a quadratic program. Fixed income securities and their valuation, statistical analysis, and portfolio selection. Discussion of the development and use of financial derivatives. Whenever practical, examples will use real market data. Numerical exercises and projects in a high-level programming environment will also be assigned.  Prerequisites: AMS 505 or AMS 510, and AMS 507. 3 credits.


Required texts and software:



  • Students will need access to the Internet to be able to attend classes via Zoom and to download course notes, assignments, financial data, and other necessary information. Students are also required to submit assignments and workshops via email.

The following may provide useful background. They are not required texts:

  • Luenberger, David G., Investment Science, Second Edition, Academic Press, 2013.


  • Sharpe, William F., Gordon Alexander & Jeffrey Baily, Investments (6th Edition), Prentice-Hall, 1998.

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Course Objectives


Financial resources must be managed in the face of uncertainties in both investment performance and funding requirements. The risk and reward of available opportunities must be modeled and estimated. These insights must then be translated into a set of specific investment decisions. All of this must be done in the context of the objectives and constraints imposed by both the organization and the larger legal and economic environment it finds itself in.


We will cover the basics of financial instruments and markets, the pricing and evaluation of financial instruments and opportunities, and address the issues involved in allocating financial resources. To bring the student up to speed in Mathematica, a tutorial lesson will be given and the course's Notes and Solutions documents will add additional tutorial material as appropriate.

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General Teaching Approach and Course Policies


The class lectures (which can be found via the Notes link for each class in the syllabus below) will develop the mathematical foundations required for successful completion of the course. We may introduce and develop additional concepts and applications not covered in the notes during the class. Homework assignments(Assignment links) and workshops (Workshop links) will also further expand the material in the class lectures. The homework solutions (Solution links) will be activated the day after the due of date of the relevant assignment.


Lecture Transcripts and Recordings


This is an online class. There will no classes held "in person". As a further learning resource for students, the links to video recordings and transcripts generated by Zoom will be made available to students. Generally, these will be provided "as is" with little editing.


Attendance Policy


To remain in compliance with Federal Regulations, Stony Brook University must determine if a student maintained eligibility for Title IV Financial Aid.  Financial Aid eligibility is determined based on a student’s attendance or participationin an academically related activity in the class.  Participation in an academically related activity includes submitting assignments, taking examinations, study groups, online instruction, and related activities. Additional information can be found here.


Additional Lectures


We may hold additional lectures during the semester to review important mathematical topics that are prerequisites for the class and to assist students with developing their Mathematica skills. Attendance at these lectures is completely voluntary. No required course material will be covered that is not already covered by the text, lectures, or various assignments.


Homework Assignments and Workshops


Homework assignments and workshops will be used to further develop the material covered during class, including many important practical applications, and will therefore introduce important new content. Homework assignments are due on or before the first class of the week after assignment. In addition to the weekly assignments, students will be assigned two workshop assignments that they will have two to three weeks to complete.

All assignments must be submitted electronically. Homework assignments are submitted to the course TA, who will let you know via Blackboard how he or she wants those assignment submitted. Workshops, however, are submitted to the course instructor via email. For all work submitted the subject line must begin with AMS-511, followed by your student ID number, and concluding with a brief description of the submission;, e.g.,


AMS-511 123456789 Assignment 03




AMS-511 123456789 Workshop 02


Also, on the files you attach to your email please ensure that the filename includes your student ID and for any Mathematica notebooks submitted that your name, student ID, and assignment description also appears prominently in the notebook.




There will be a final examination. Proctoring arrangements for how that examination will be handled are still under development. For the examination students will be able to bring in an 8.5" x 11" sheet of paper with whatever content he or she desires for use during the test; however, this sheet must be generated by the student him- or herself. Students may use calculators during the examinations.




Homework assignments and workshops will be graded Pass-Fail. The homework assignments seek to provide students with practice and help to identify any weak points to ensure they can develop the skills necessary for successful completion of the course. Thus, if a reasonable attempt is made to solve a problem, you will receive full credit. Homework assignments submitted late receive no credit.
Examinations will be graded A, A-, B+, B, B-, C, F. I do not follow a strict grade distribution. If you are diligent and complete all homework and workshop assignments to receive full credit, then this will go a long way towards increasing your final grade.


The contribution of each to the final grade is as follows:


  • Homework Assignments -- 20%


  • Workshop -- 40%


  • Final Examination -- 40%


Positive trends in a student's performance will, however, receive due consideration. The course will be graded A, A-, B+, B, B-, C, F.


Problems Affecting Attendance or Performance


Throughout our time together the sooner you inform me of any problem, personal or academic, which may affect your attendance or performance, the better the chance we have of solving it together. Please do not delay in talking to me. I am here to help. I want all of you to succeed.


Academic Honesty

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the Academic Judiciary web site at http://www.stonybrook.edu/commcms/academic_integrity/index.html.


Students with Disabilities

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: https://ehs.stonybrook.edu//programs/fire-safety/emergency-evacuation/evacuation-guide-disabilities  and search Fire Safety and Evacuation and Disabilities. 

Office of Diversity and Affirmative Action

Stony Brook University is committed to a learning and working environment in which all members of our community can thrive. Maintaining an environment that is free from discrimination and sexual violence is a major part of that commitment.


To that end, the University is providing education and awareness training for all members of our community to help continue to foster the positive environment that is key to your success here at Stony Brook. More information about your rights and responsibilities can found at the Office of Diversity and Affirmative Action website.


Class Schedule & Assignments

The schedule planned for this semester is listed below; however, this schedule will be adjusted as needed throughout the semester if certain topics take up more or less time than planned. 

Under the Documents heading links are:


  • Notes - These are Mathematica notebooks covering the class notes for that class's lecture. Every attempt will be made to link the course notes in advance of the class.


  • Assignment - These are Mathematica notebooks containing the week's assignments; unless otherwise noted, they are due on or before the next class meeting, must be in notebook format, and should be emailed to the TA.
  • Solutions - The solutions of each lecture's assigments will be linked no earlier than the day after the respective due date. These solutions are usually Mathematica notebooks.


  • Workshop - Each of the two workshops will be specified in a Mathematica notebook. Both workshops will require that you download actual financial data from the Internet.


  • Workshop Solution - After each workshop due date has passed a sample solution of the workshop will be linked. These solutions are usually Mathematica notebooks.


  • Additional documents required such as tutorials, data needed for assignments, additional software and so forth will also be linked as needed.


Mathematica Stylesheet Required


To properly use the notebooks below you will need to download a copy of my StonyBrook.nb stylesheet and install it on your system. Type in "install stylesheet" in the search box of Mathematica's Documentation Center (accessed under Help on the main menu) for detailed instructions on how to install a stylesheet on your system. Please see me if you have any problems, and I will help you with the installation.

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This page is regularly updated throughout the semester. Remember to reload this page so that you have the most current version.




Mathematica Tutorial

Introduction to Markets

Time Value of Money

Basic Wolfram Language Tutporial (Mathematica)



Topics in Time Value of Money

Bonds, Mortgages, and Other Forms of Debt

Additional Features and Financial Tools in the Wolfram Language



Portfolio Optimization
FinancialData[ ] Function


Capital Asset Pricing Model
Multi-Factor Models
Risk Measures


Introduction to Derivatives
Binomial Lattice Models of Asset Dynamics
Introduction to Stochastic Calculus and Itô's Lemma

Additional Topics in Options Theory
The Black-Scholes-Fisher Pricing
FinancialDerivative[ ] Function
Numerical Methods
Implied Volatility


Options Strategies for Risk Management
Jump Diffusions and Stochastic Volatility
Valuation of Path Dependent Options


Credit Risk
Structural Models
Intensity Models
Rating Agencies
Credit Derivatives


Power Laws
Cash Flows in Graphs
Optimal Growth and Portfolio Dynamics
Kelly Betting

AI/ML Models in Mathematica
Natural Language Processing