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
Course Description:
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.
M |
Dr. Martin Luther King, Jr. Day ~ University Closed |
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Su-Su |
Spring Recess ~ No Classes Scheduled ~ University Open |
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T |
Last Day to Withdraw from this course |
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F |
Good Friday ~ University Closed |
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T |
Classes follow a Friday Schedule, Last Day of Classes |
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W |
Reading Day |
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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 |