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AMS 511 - Foundations of Quantitative Finance

Fall 2019

Prof. Robert J. Frey, Instructor




Course Lecture:

    Wednesday, 02:30 PM - 05:20 PM

    Frey Hall 211


Office Hours:

     By Appointment

Teaching Assistant:

    Zeyu Cao



Office Hours:

    Thursday, 10:00 AM - Noon

    Room B-148

This page is regularly updated throughout the semester. Remember to reload this page so 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.


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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 download course notes, assignments, and financial data, and to submit certain assignments via email.

The following 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.


  • Don, Eugene, Schaum's Outline of Theory and Problems of  Mathematica, McGraw-Hill, 2001.

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Course Objectives


Financial resources must be managed in the face of uncertain investmemt performance and future consumption. The risk and reward of available investments 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 almost all of Luenberger's text with additional material contained in the Course Notes that can be downloaded for each lecture. This 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 in the face of an uncertain future. To bring the student up to speed in Mathematica, a tutorial lesson will be given and the Course Notes and Course Solutions documents we add will 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 will introduce and develop many additional economic concepts and practical applications not covered in the textbook through theory and examples presented during class. Homework assignments(Assignment links) and workshops (Workshop links) will also further expand the material in the text and class lectures. The homework solutions (Solution links) will be activated the day after the due of date of the relevant assignment.


Addendance 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.  Participationin 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 so will 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. Mr. Li will let you know via Blackboard how he wants those assignment submitted. Workshops 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 that your name, student ID, and assignment description also appears prominently in the notebook.




There will be two examinations, a mid-term and a final. For in-class examinations 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. 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 -- 10%


  • Workshop 1 -- 10%


  • Workshop 2 -- 15%


  • Midterm Examination -- 20%


  • Final Examination -- 35%


Positive trends in a student's performance will, however, receive due consideration.


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.


Academic Honesty


The University regards academic honesty as essential for all members of the academic community. Violations are punishable by severe penalties, including dismissal from the University. Policy requires that all instructors and TAs report all suspected cases of academic dishonesty to the appropriate Academic Judiciary Committee. If you have any questions as to what constitutes dishonest activity, then do not hestitate to consult with any faculty member. Seeking advice will not in itself be viewed as evidence of inappropriate behavior.

There are many forms of academic dishonesty; however, most reduce to a case in which one student passes off the work of another as if it were his or her own. There is nothing wrong with using others' ideas or seeking help as long as that debt is acknowledged. In fact, students are urged to form study groups to help them work through the course material and assignments more efficiently and effectively and are encouraged to seek academic guidance from the course instructor and TA or from fellow students at appropriate times. Wholesale copying of another student's assignment work or cheating on an examination are entirely different matters. Further information can be found at the Academic Judiciary.

Americans with Disabilities Act (ADA) Notification

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, Disability Support Services, and Environmental Health and Safety.


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 responsibilites can found at the Office of Diversity and Affirmative Action website.


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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. The letter "I" is used to indicate Investment Science, and students must read the chapters indicated under Coverage for each week before coming to class. The Assignment & Comments column contains any special information associated with each lecture.

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. The Notes cover the assigned readings but also include material and examples intended to amplify or extend the content presented in the textbook. They are not a substitute for studying the text or attending class. Also note that the Class Notes may span more than one class meeting.


  • Coverage - Readings in An Elementary Introduction to the Wolfram Language are identified with a "W". The chapters and sections to be worked through follow each letter.


  • 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. These notebooks contain problems that are either created by the instructor or which are drawn from Luenberger's Investment Science.


    • It stronly recommended that students work through the all of the exercises in each week's readings in Wolfram's An Elementary Introduction to the Wolfram Language. They are for the student's benefit and should not be submitted.


  • 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.





Introduction to Markets

Time Value of Money

Basic Wolfram Language Features (Mathematica)




Topics in Time Value of Money

Bonds, Mortgages, and Other Forms of Debt

Financial Tools in the Wolfram Language




Bonds, Yield Curve

Dividend Discount Models

Lattice Models




FinancialBond[ ] Function

Multivariate Normal Distributions

Mean-Variance Portfolio Optimization




Capital Asset Pricing Model

Arbitrage Pricing Theory and Factor Models

Risk Measures including Value-at-Risk and Expected Shortfall

Quadratic Programming Package

Value-at-Risk and Related Measures

Coherent Risk Measures


 Mid-Term Review


Additional Risk Topics

Mid-Term Review




Solutions to the Mid-Term



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



Additional Topics in Options Theory
The Black-Scholes Pricing Formula
Mathematica's FinancialDerivative[] Function
Numerical Methods
Implied Volatility




Option Strategies

Model Extensions

Optimal Growth

Portfolio Dynamics


Notes & Workshop

  Monte Carlo Simulation of Exotic Options
Additional Topics in Options

EM Algorithm Tutorial
Neural Network Tutorial
Neural Network Example
Final Exam Sample

  Machine Learning (Distribution Fitting with the EM Algorithm)
Neural Network Tutorial
Artificial Intelligence (Building a Factor Model with a Neural Network)
Final Examples