625.641.81 - Mathematics of Finance

Expanded Course Description

Prerequisites 

Multivariate calculus and an introductory course in probability and statistics (such as 625.403). Some familiarity with optimization is desirable but not necessary. 

Course Structure

The course materials are divided into modules. The Modules can be accessed by clicking Modules on the menu. A module will have several sections including the overview, content, readings, discussions, and assignments. Students are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted on the Course Outline page. Students should regularly check the Calendar and Announcements for assignment due dates. 

Course Topics

•  Introduction to Deterministic Cash Flow Analysis
•  Fixed-Income Securities
• Capital Budgeting and Dynamic Cash Flow
• Capital Asset Pricing Model
• Other Pricing Models
• Risk Measures
• Utility Functions
• Forwards, Futures and Swaps
• Model of Asset Dynamics
• Black Scholes Theory I
• Black Scholes Theory II
  

Course Goals

• To introduce the main financial instruments and the mathematical tools used in pricing them.
• To study various investment problems. 

Course Learning Outcomes (CLOs)

• Evaluate and price various financial securities and their derivatives.
• Construct optimal portfolios.
• Study various asset pricing Models.

Textbooks

Required 

David G. Luenberger (2014). Investment Science (2rd Ed.). Oxford University Press. 

ISBN-13: 978-0-19-974008-6. 

Textbook information for this course is available online through the appropriate bookstore website: For online courses, search the MBS website at http://ep.jhu.edu/bookstore. 

Required Software

MATLAB 

You will need access to a recent version of MATLAB. The MATLAB Total Academic Headcount (TAH) license is now in effect. This license is provided at no cost to you. Send an email to software@jhu.edu to request your license file/code. Please indicate that you need a standalone file/code. You will need to provide your first and last name, as well as your Hopkins email address. You will receive an email from Mathworks with instructions to create a Mathworks account. The MATLAB software will be available for download from the Mathworks site. 

Student Coursework Requirements

It is expected that each module will take approximately 7–9 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 2–3 hours per week) as well as some outside reading, listening to the audio annotated slide presentations (approximately 1–2 hours per week), and writing assignments (approximately 1–2 hours per week). 

This course will consist of five basic student requirements: 

Group Project (15% of Final Grade Calculation)
Each student should join a group of at least 2 or at most 4 students. Each group should prepare and present a report about an investment problem.

Preparation and Participation (Module Discussions) (10% of Final Grade Calculation) 

Each student is responsible for carefully reading all assigned material and being prepared for discussion. The majority of readings are from the course text. Additional reading may be assigned to supplement text readings. 

Post your initial response to the discussion questions by the evening of day 3 for that module week. Posting a response to the discussion question is part one of your grade for module discussions (i.e., Timeliness). 

Part two of your grade for module discussion is your interaction (i.e., responding to classmate postings with thoughtful responses) with at least two classmates (i.e., Critical Thinking). Just posting your response to a discussion question is not sufficient; we want you to interact with your classmates. Be detailed in your postings and in your responses to your classmates' postings. 

Feel free to agree or disagree with your classmates. Please ensure that your postings are civil and constructive. 

I will monitor module discussions and will respond to some of the discussions as discussions are posted. 

Evaluation of preparation and participation is based on contribution to discussions. Preparation and participation is evaluated by the following grading elements:

1. Timeliness (50%)
2. Critical Thinking (50%)

Preparation and participation is graded as follows: 

10–9 = A—Timeliness [regularly participates; all required postings; early in discussion; throughout the discussion]; Critical Thinking [rich in content; full of thoughts, insight, and analysis]. 

8–9 = B—Timeliness [frequently participates; all required postings; some not in time for others to read and respond]; Critical Thinking [substantial information; thought, insight, and analysis has taken place]. 

6–7 = C—Timeliness [infrequently participates; all required postings; most at the last minute without allowing for response time]; Critical Thinking [generally competent; information is thin and commonplace]. 

Assignments (25% of Final Grade Calculation) 

Assignments will include a quantitative problem sets. Include a cover sheet with your name and assignment identifier. Also include your name and a page number indicator (i.e., page x of y) on each page of your submissions. Each problem should have the problem statement, assumptions, computations, and conclusions/discussion delineated. All Figures and Tables should be captioned and labeled appropriately. 

All assignments are due according to the dates in the Calendar. 

Late submissions will be reduced by one letter grade for each week late (no exceptions without prior coordination with the instructors). 

Qualitative assignments are evaluated by the following grading elements: 

1. Each part of question is answered (20%) 
2. Writing quality and technical accuracy (30%) (Writing is expected to meet or exceed accepted graduate-level English and scholarship standards. That is, all assignments will be graded on grammar and style as well as content). 
3. Rationale for answer is provided (20%) 
4. Examples are included to illustrate rationale (15%) (If a student does not have direct experience related to a particular question, then the student is to provide analogies versus examples).
5. Outside references are included (15%)

Qualitative assignments are graded as follows: 

100–90 = A—All parts of question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [rich in content; full of thought, insight, and analysis]. 

89–80 = B—All parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [substantial information; thought, insight, and analysis has taken place]. 

79–70=C—Majority of parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [generally competent; information is thin and commonplace]. 

<70=F—Some parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [rudimentary and superficial; no analysis or insight displayed]. 

Quantitative assignments are evaluated by the following grading elements: 

1. Each part of question is answered (20%) 
2. Assumptions are clearly stated (20%) 
3. Intermediate derivations and calculations are provided (25%) 
4. Answer is technically correct and is clearly indicated (25%)
5. Answer precision and units are appropriate (10%)

Quantitative assignments are graded as follows: 

100–90 = A—All parts of question are addressed; All assumptions are clearly stated; All intermediate derivations and calculations are provided; Answer is technically correct and is clearly indicated; Answer precision and units are appropriate. 

89–80 = B—All parts of question are addressed; All assumptions are clearly stated; Some intermediate derivations and calculations are provided; Answer is technically correct and is indicated; Answer precision and units are appropriate. 

79–70=C—Most parts of question are addressed; Assumptions are partially stated; Few intermediate derivations and calculations are provided; Answer is not technically correct but is indicated; Answer precision and units are indicated but inappropriate. 

<70=F—Some parts of the question are addressed; Assumptions are not stated; Intermediate derivations and calculations are not provided; The answer is incorrect or missing; The answer precision and units are inappropriate or missing. 

Midterm Exam (25% of Final Grade Calculation) 

The midterm exam will be available in Module 6. Students will have one week to complete the exams and they will be due by 5 PM exactly one week from their release. Students may use the course text to complete the exams. 

The exam is evaluated by the following grading elements: 

1. Each part of question is answered (20%) 
2. Writing quality and technical accuracy (30%) (Writing is expected to meet or exceed accepted graduate-level English and scholarship standards. That is, all assignments will be graded on grammar and style as well as content). 
3. Rationale for answer is provided (20%) 
4. Examples are included to illustrate rationale (15%) (If a student does not have direct experience related to a particular question, then the student is to provide analogies versus examples).
5. Outside references are included (15%)

Exams are graded as follows: 

100–90 = A—All parts of question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [rich in content; full of thought, insight, and analysis]. 

89–80 = B—All parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [substantial information; thought, insight, and analysis has taken place]. 

79–70 = C—Majority of parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [generally competent; information is thin and commonplace]. 

Final (25% of Final Grade Calculation) 

The final exam will be available in the next-to-last Module. Students will have one week to complete the exams and they will be due by 5 PM exactly one week from their release. Students may use the course text to complete the exams. 

The exam is evaluated by the following grading elements: 

1. Each part of question is answered (20%)
2. Writing quality and technical accuracy (30%) (Writing is expected to meet or exceed accepted graduate-level English and scholarship standards. That is, all assignments will be graded on grammar and style as well as content). 
3. Rationale for answer is provided (20%) 
4. Examples are included to illustrate rationale (15%) (If a student does not have direct experience related to a particular question, then the student is to provide analogies versus examples).
5. Outside references are included (15%)

Exams are graded as follows: 

100–90 = A—All parts of question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [rich in content; full of thought, insight, and analysis]. 

89–80 = B—All parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [substantial information; thought, insight, and analysis has taken place]. 

79–70 = C—Majority of parts of the question are addressed; Writing Quality/ Rationale/ Examples/ Outside References [generally competent; information is thin and commonplace]. 

Grading Policy

Student assignments are due according to the dates in the Calendar and Assignments items in the corresponding modules. I will make every effort to post grades one week after assignment due dates. 

A grade of A indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of assignments and discussion in every week. 

A grade of B indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course. 

Course Policies

Academic Misconduct Policy 

Students should read policies pertaining to academic misconduct and netiquette at http://ep.jhu.edu/genpolguid. Please read below how the Academic Misconduct Policy applies to your course. 

Collaborations and discussions between students are key ingredients to success in a graduate course. You are encouraged to discuss the course material with each other as you sort through concepts that may be difficult to comprehend or controversial. However, the line between collaboration and cheating needs to be carefully delineated. Whenever you turn in work with your name on it to be evaluated, graded and included in your record it must represent an individual effort by you alone. If you include direct quotes from any source in your discussions, written assignments, the final exam, or any other submission for which you will receive a grade you must provide attribution. Students using published material without reference, or copying the work of another individual will receive a warning at the first incident. Any further incidents will result in the student receiving a zero on the assignment and the matter will be referred to the Associate Dean. Contact us if you have any questions, no matter how slight, about this policy, or if you have questions about a particular assignment. 

Plagiarism

Plagiarism is defined as taking the words, ideas or thoughts of another and representing them as one's own. If you use the ideas of another, provide a complete citation in the source work; if you use the words of another, present the words in the correct quotation notation (indentation or enclosed in quotation marks, as appropriate) and include a complete citation to the source. See the course text for examples. 

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.