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Math 606: Term Structure Models
Spring 2019 Graduate Course Syllabus

NJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.

Course Information

Course Description: This course will explore the structure, analysis, and use of financial derivative instruments deployed in investment strategies and portfolio risk management. Topics include continuous time dynamics, arbitrage pricing, martingale methods, and valuation of European, American, and path dependent derivatives. Effective From: Fall 2011.

Number of Credits: 3

Prerequisites: Fin 641 Derivatives, Math 605 Stochastic Calculus, or permission of the instructor.

Course-Section and Instructors

Course-Section Instructor
Math 606-102 Professor Professor A. Pole

Office Hours for All Math Instructors: Spring 2019 Office Hours and Emails

Required Textbooks:

Title Fixed Income Securities
Author Veronesi
Publisher John Wiley & Sons, Inc.
ISBN # 978-0470109106

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, April 8, 2019. It will be strictly enforced.


Course Objectives: This course develops the mathematical structure of interest rate models and explores the considerable hurdles involved in practical implementation. Short rate models, single and multifactor; the Heath-Jarrow-Morton framework; and Libor market models are examined.

Course Outcomes

After completing this course students will be able to:

Course Assessment: Assessment of objectives is achieved through homework assignments, a project [TBD], and two examinations: a midterm exam and a comprehensive final exam.


DMS Course Policies: All DMS students must familiarize themselves with, and adhere to, the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly.

Grading Policy: The final grade in this course will be determined as follows:

Homework Assignments 30%
Project 10%
Midterm Exam 30%
Final Exam 30%

Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced. AttendanceNote

Exams: There will be one midterm exam held in class during the semester and one comprehensive final exam. Exams are held on the following days:

Midterm Exam Week 8
Final Exam Period May 10 - 16, 2019

The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.

Makeup Exam Policy: To properly report your absence from a midterm or final exam, please review and follow the required steps under the DMS Examination Policy found here:

Cellular Phones: All cellular phones and other electronic devices must be switched off during all class times.

Additional Resources

Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.

If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at The office is located in Fenster Hall Room 260. A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.

For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:

Important Dates (See: Spring 2019 Academic Calendar, Registrar)

Date Day Event
January 22, 2019 T First Day of Classes
February 1, 2019 F Last Day to Add/Drop Classes
March 17 - 24, 2019 Su - Su Spring Recess - No Classes, NJIT Open
April 8, 2019 M Last Day to Withdraw
April 19, 2019 F Good Friday - No Classes, NJIT Closed
May 7, 2019 T Friday Classes Meet/ Last Day of Classes
May 8 & 9, 2019 W & R Reading Days
May 10 - 16, 2019 F - R Final Exam Period

Course Outline

Week 1

Overview of interest rates and fixed income instruments & markets

Week 2

Yield curve construction & modeling: Bootstrap; Nelson-Siegel & Svensson curves

Week 3 & 4

Principal Components Analysis; Factor modeling & case study

[Veronesi Chapter 3, 4]
Week 5

Binomial tree models for interest rates; coupon bond pricing on trees;
Market price of interest rate risk; risk neutral pricing and dynamic replication

[Veronesi Chapter 9, 10]
Week 6

Risk neutral trees and derivative pricing; discrete Ho-Lee & Black-Derman-Toy;
Pricing caps, floors, swaps & swaptions

[Veronesi Chapter 11]
Week 7

Pricing American options on binomial interest rate trees; dynamic replication of callable bonds; option replication; non-convexity; option adjusted spread

[Veronesi Chapter 12]

Briefly, as time permits:
Monte Carlo simulation on interest rate trees; pricing path dependent options & application to index amortizing swaps; pricing mortgage backed securities

[Veronesi Chapter 13]
Week 8
Week 9

Martingale valuation & change of numeraire with interest rates

[Pelsser Chapter 1, 2; Björk Chapter 22]
Week 10 & 11

Short rate models; affine class;
Ho-Lee; Vasicek; Cox-Ingersoll-Ross; Hull-White; Dothan; BDT; Black-Karasinski
Forward measure;

[Björk Chapter 23, 24; Veronesi Chapter 15, 19, 20]
Week 12, 13, & 14

HJM methodology;
Black model; cap & caplet pricing; LIBOR market models; volatility structures
Jamshidian decomposition; two factor models;

[Veronesi Chapter 21, 22]
Week 15

Updated by Professor A. Pole - 1/21/2019
Department of Mathematical Sciences Course Syllabus, Spring 2019