NJIT HONOR CODE

All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor code very seriously and enforces it strictly.  This means 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 Honor Code, students are obligated to report any such activities to the Instructor.

Math 604: Mathematical Finance    

Instructor: Prof. Pole

Textbook: Arbitrate Theory in Continuous Time by Bjork, ISBN 978-0199574742

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

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

 

       

 

MATH DEPARTMENT CLASS POLICIES LINK

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. For DMS Course Policies, please click here.

January 21, 2013

M

Dr. Martin Luther King, Jr. Day ~ University Closed

March 17-24, 2013

Su-Su

Spring Recess ~ No Classes Scheduled ~ University Open

March 26, 2013

T

Last Day to Withdraw from this course

March 29, 2013

F

Good Friday ~ University Closed

May 7, 2013

T

Classes follow a Friday Schedule, Last Day of Classes

May 8, 2013

W

Reading Day

May 9-15, 2013

T-W

Final Exams

 


Course Outline

 

Week Topic
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;

[Bjork Chapter 1 and other material]

2 Binomial model, one period and multi-period; arbitrage condition; replicating portfolios; risk neutral valuation; contingent claims; complete market;  martingale measure

[Bjork Chapter 2]

3

Further developments in the Binomial Market Model

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

[Bjork, Kennedy Chapter 2]

4 Generalized multi-asset & multi-state discrete model

[Bjork Chapter 3,4]

5 Stochastic calculus summary review and illustration

[Bjork Chapter 4, ...]

6 Stochastic Differential Equations

[Bjork Chapter 5]

7 Portfolio Dynamics: the continuous time analogue of concepts in classes 1-4 including arbitrage pricing & development of Black-Scholes PDE

[Bjork Chapter 6,7]

8 MID TERM EXAM
9

More Black-Scholes analysis:

Options on futures; American options; Completeness & Hedging; Parity Relations & Delta Hedging;

[Bjork Chapter 7,8,9 

10&11 Martingale Approach to Arbitrage

Constructing risk neutral measure from call prices

[Bjork Chapter 10, 11, 12]

12&13 Exotic Derivatives

[Musiela & Rutkowski Chapter 6, Epps Chapter 7,…]

14

Incomplete Markets; Dividends ;Stochastic Volatility

[Bjork Chapter 15, 16]

15 FINAL EXAM
   

 

 Prepared by Prof. Andrew Pole

Last revised: January 8, 2013