Math 604: Mathematical Finance
Spring 2018 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 604-102 |
Professor A. Pole |
Office Hours for All Math Instructors: Spring 2018 Office Hours and Emails
Required Textbooks:
Title |
Arbitrage Theory in Continuous Time |
Author |
Bjork |
Edition |
3rd |
Publisher |
Oxford University Press |
ISBN # |
978-0199574742 |
University-wide Withdrawal Date:The last day to withdraw with a w is Monday, April 2, 2018. It will be strictly enforced.
Course ASSESSMENT CRITERIA
Course Objectives: This course explores the mathematical structure and analysis of models for financial markets, where the primary goal is valuation of financial derivative instruments deployed in investment strategies and portfolio risk management. Topics include discrete and continuous time dynamics, static and dynamic hedging, portfolio replication of claims, arbitrage pricing, martingale methods, and valuation of European, American, and path dependent derivatives.
Course Outcomes
After completing this course students will be able to:
- Describe the mathematical structure of regularly traded financial derivative securities, including European, American and exotic options.
- Describe and demonstrate risk neutral (arbitrage) pricing of derivative securities.
- Describe and demonstrate the analysis of the standard discrete and continuous time derivative security pricing models.
Course Assessment: Assessment of objectives is achieved through homework assignments, a project [TBD], and two examinations: a midterm exam and a comprehensive final exam.
Policies
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.
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 7 |
Final Exam Period |
May 5 - 10, 2018 |
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 lyles@njit.edu. 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 2018 Academic Calendar, Registrar)
Date |
Day |
Event |
January 16, 2018 |
T |
First Day of Classes |
January 22, 2018 |
M |
Last Day to Add/Drop Classes |
March 11 - 18, 2018 |
Su - Su |
Spring Recess - No Classes/ University Closed |
March 30, 2018 |
F |
Good Friday - No Classes/ University Closed |
April 2, 2018 |
M |
Last Day to Withdraw |
May 1, 2018 |
T |
Friday Classes Meet - Last Day of Classes |
May 2 - 3, 2018 |
W - R |
Reading Days |
May 4 - 10, 2018 |
F - R |
Final Exam Period |
Course Outline
Week 1 |
Introduction & Overview:
Derivative Securities; primary assets; Law of one price; no free lunch;
Overview of derivatives pricing: arbitrage pricing, static & dynamic replication;
Self-financing portfolio; Black Scholes Merton; risk-neutral/martingale pricing;
[Björk Chapter 1 and other material] |
Week 2 |
Binomial model, one period and multi-period; arbitrage condition; replicating portfolios; risk neutral valuation; contingent claims; complete market; martingale measure
[Björk Chapter 2] |
Week 3 |
Further developments in the Binomial Market Model: hedge portfolios;
Real world vs risk neutral probability; CRR and JR parameterization;
Demonstration of European and American put valuation on trees; simulation;
[Utility maximization for 1-period model]
[Björk, Kennedy Chapter 2] |
Week 4 |
Early exercise (American) and barrier options: Valuation proofs in binomial market model;
Change of probability in binomial model; discussion of generalization & Radon-Nikodým;
Path dependent claims in binomial model;
Examples of martingale measure calculation
[Professor supplied material] |
Week 5 |
N-Asset – M-state 1 period model; Arrow-Debreu state prices;
Summary of discrete model analysis
[Björk Chapter 3 & other material] |
Week 6 |
Stochastic calculus summary review and illustration;
Stochastic Differential Equations
[Björk Chapter 4, 5] |
Week 7 |
MIDTERM EXAM
|
Week 8 |
Portfolio Dynamics: the continuous time analogue of concepts in classes 1-5 including arbitrage pricing & development of Black-Scholes PDE
[Björk Chapter 6, 7] |
Week 9 |
More Black-Scholes analysis:
Options on futures; American options; Completeness & Hedging; Parity Relations & Delta Hedging;
[Björk Chapter 7,8,9] |
Week 10, 11 |
Martingale Approach to Arbitrage;
Constructing risk neutral measure from call prices
[Björk Chapter 10, 11, 12 (parts)] |
Week 12, 13 |
Exotic Derivatives
[Musiela & Rutkowski Chapter 6, Epps Chapter 7] |
Week 14 |
Incomplete Markets; Dividends; Stochastic Volatility
[Björk Chapter 15, 16] |
Week 15 |
FINAL EXAM |
Updated by Professor A. Pole - 1/18/2018
Department of Mathematical Sciences Course Syllabus, Spring 2018