553.445/645: Interest Rate and Credit Derivatives

Course Description

553.445/645 Interest Rate and Credit Derivatives:  This is the second of a two-course sequence

devoted to the mathematical modeling of securities and the markets in which they are created and

exchanged.  The focus in this course turns to interest rate derivatives and the credit markets.  The

martingale approach to risk-neutral valuation is covered, followed by interest rate derivatives, models of the short rate process, and term structure models (including Heath, Jarrow, & Morton and the Libor

Market Model); analysis of bonds with embedded options and other interest rate derivatives (e.g., caps, floors, swaptions).  Credit risk and credit derivatives, including copula models of time to default, credit

default swaps, and a brief introduction to collateralized debt obligations.  An important component of this course are the computational methods associated with the main topics.  This includes data and time

series analysis (e.g., estimation of volatilities); developing binomial and trinomial lattices; and derivative

analysis schemes, including numerical approaches to solving the partial differential equations of derivatives.

Prerequisites

The recommended prerequisite is 553.644 (Introduction to Financial Derivatives); otherwise, a strong

familiarity of the financial markets and instruments along with a firm understanding of calculus, probability and differential equations.  Usually, students in the MSE Financial Mathematics program have what is

required and the instructor will typically grant approval to enroll.

Course Goals

Interest rate and credit derivatives are fundamental to modern finance and the management of capital flows and their application.  This course will apply mathematical modeling and analysis techniques to  interest rate and credit derivatives so that their valuation, risk characterization, analysis and context in financial structures can be engineered and quantitatively described.

Course Objectives

By the end of this course, you will be able to:

•     Characterize the fundamental modeling attributes of interest rate and credit derivatives.

•     For interest rate derivatives, synthesize a set of Standard Market Models (along with appropriate variations and adaptations) from the fundamental Equivalent Martingale Measure Result.

•     Develop term structure models based on the short rate and forward rate models - to include the Heath, Jarrow, Morton model and the Libor Market Model.

•     For credit derivatives, synthesize a set of models suitable for characterizing time to default for correlated entities

•     Develop credit structuring methodologies for credit default swaps and aggregates of credit default entities; specifically including cash and synthetic credit default obligations (CDO).

Course Structure

The course materials are divided into modules. The Modules can be accessed by clicking Course Content tab on the left menu of Blackboard. A module will have several sections which may include the overview,   lecture content, readings, discussions, and assignments. Students are encouraged to preview all sections of the module at the beginning of each week.

TEXTBOOKS

Required

Hull, John C (2022).  Options, Futures, and Other Derivatives (11th  ed.): Prentice Hall

ISBN- 13:  978- 1292410654

ISBN- 10:  1292410655

Textbook information for this course is available online through the appropriate bookstore website.

Recommended

Hull, John C (2018).  Student Solutions Manual for Options, Futures, and Other Derivatives (10th  ed.): Prentice Hall

ISBN- 13:  978-0134472089

ISBN- 10:  0134472089

Alternative - Some have access to an earlier Hull edition (as follows).  As that edition is very similar to the 11th, I will provide indication as to the readings, etc. of the 10th  edition corresponding to the 11th.

Hull, John C (2018).  Options, Futures, and Other Derivatives (10th  ed.): Prentice Hall

ISBN- 13:  978-0133456318

ISBN- 10:  0133456315

Technical Requirements

Students should refer to “ Help” & “Support” tabs in Blackboard for a general listing of all the course technical requirements.

Student Coursework Requirements

It is expected that each module will take approximately 10 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; attending lecture or viewing the lecture recordings (3 hours per week): and completing writing assignments (approximately 3 hours per week).

This course will consist of three basic student requirements:

1.   Assignments (1/3 of Final Grade Calculation)

Assignments may include a mix of qualitative assignments (e.g. literature/paper reviews, model summaries), quantitative assignments – problem sets, and case study updates. Ideally, and

where appropriate, 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 assigned.

Late submissions may be reduced by one letter grade for each week late (no exceptions without prior coordination with the instructor/TA).

If, after submitting a written assignment a student is not satisfied with the grade received, the

student is encouraged to contact the TA to discuss the submission.  Often, a student is welcomed to redo/correct the assignment and resubmit it. If the resubmission results in a better grade, that    grade will be substituted for the previous grade.

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 graded as follows:

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.

2.   Exams (2/3 of Final Grade Calculation, combined from 1/3 for Midterm and 1/3 for Final)

The midterm exam will be completed during Module 7 at a time corresponding the regular class

meeting time. The final exam will be completed during the exam period specified by the Registrar.

The exams are evaluated by the following grading elements:

1.   Each part of question is answered correctly (50%)

2.   Rationale (work) for answer is provided (50%)

Exams are graded as follows:

100–90 = A—All parts of all questions are addressed;

89–80 = B—All parts of most questions are addressed;

79–70 = C— Majority of parts of most questions are addressed;

<70 = F—Only Some parts of some of the questions are addressed;.

Grading

Student assignments are due according to the dates assigned. The TA will post grades one week after assignment due dates.

We generally do not directly grade spelling and grammar. However, egregious violations of the rules of

the English language will be noted without comment. Consistently poor performance in either spelling or   grammar is taken as an indication of poor written communication ability that may detract from your grade.

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.

We use a +/- grading system (see “Grading System”, Graduate Programs catalog). Example:

100–98 = A+

97–94 = A

93–90 = A−

89–87 = B+

86–83 = B

82–80 = B−

79–70 = C

<70 = F

However, a grade of “A+” requires more than an excellent score (98- 100).  The instructor will also

evaluate the students continuing level of excellence beyond what is required in the course – especially, as it relates to participation, contribution, and insight.

Final grades will be determined by the following weighting:

Help & Support

Students should refer to Help & Support on the left menu for a listing of all the student services and support available to them.

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 Graduate as well as Undergraduate Students:

• For Undergraduates:http://e-catalog.jhu.edu/undergrad-students/student-life-policies/

• For Graduate students:http://e-catalog.jhu.edu/grad-students/graduate-specific-policies/

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.

Professor Audley is seriously committed to ethical behavior as it is a keystone requirement in the financial industry. Accordingly, serious breaches of academic ethics will be recommended for assigning a grade of “F” in the course.

Policy on Disability Services

Johns Hopkins University (JHU) is committed to creating a welcoming and inclusive environment for

students, faculty, staff and visitors with disabilities.  The University does not discriminate on the basis of race, color, sex, religion, sexual orientation, national or ethnic origin, age, disability or veteran status in   any student program or activity, or with regard to admission or employment. JHU works to ensure that    students, employees and visitors with disabilities have equal access to university programs, facilities,

technology and websites.

Under Section 504 of the Rehabilitation Act of 1973, the Americans with Disabilities Act (ADA) of 1990   and the ADA Amendments Act of 2008, a person is considered to have a disability if (1) he or she has a physical or mental impairment that substantially limits one or more major life activities (such as hearing, seeing, speaking, breathing, performing manual tasks, walking, caring for oneself, learning, or

concentrating); (2) has a record of having such an impairment; or (3) is regarded as having such an

impairment class. The University provides reasonable and appropriate accommodations to students and  employees with disabilities.  In most cases, JHU will require documentation of the disability and the need for the specific requested accommodation.

The Disability Services program within the Office of Institutional Equity oversees the coordination of

reasonable accommodations for students and employees with disabilities, and serves as the central point  of contact for information on physical and programmatic access at the University. More information on this policy may be found athttp://web.jhu.edu/administration/jhuoie/disability/index.htmlor by contacting (410)  516-8075.