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 606 Term Structure Models
Course Description: This course will develop the mathematical structure of interest rate models and explore the considerable hurdles involved in practical implementation. Short rate models, single and multifactor; the Heath-Jarrow-Morton framework; and modern Libor market models will be examined. 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.
| 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 |
Overview of interest rates and fixed income
instruments & markets;
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| 2 |
Bootstrap; Nelson-Siegel & Svensson curves |
| 3 |
Principal Components Analysis; Factor modeling & case study [Veronesi Chapater 3, 4] |
| 4 |
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] |
| 5 |
Risk neutral trees and derivative pricing; discrete Ho-Lee & Black-Derman-Toy; Pricing caps, floors, swaps & swaptions [Veronesi Chapter 11] |
| 6 |
Pricing American options on binomial interest rate trees; dynamic replication of callable bonds; option replication; non-convexity; option adjusted spread [Veronesi Chapter 12] |
| 7 |
Monte Carlo simulation on interest rate trees; pricing path dependent options & application to index amortizing swaps; pricing mortgage backed securities [Veronesi Chapter 13] |
| 8 | MID TERM EXAM |
| 9 |
Martingale valuation & change of numeraire with interest rates; [Pelsser Chapter 1, 2; Bjork Chapter 22] |
| 10&11 |
Short rate models; affine class; Ho-Lee; Vasicek; Cox-Ingersoll-Ross; Hull-White; Dothan; BDT; Black-Karasinski Forward measure; [Bjork Chapter 23, 24] |
| 12 |
HJM methodology; Black model; cap & caplet pricing; LIBOR market
models; volatility structures |
| 13 |
Jamshidian decomposition; Two factor models |
| 14 |
Estimation: generalized method of moments;
maximum likelihood |
| 15 | FINAL
EXAM |