16:642:612-02 Selected Topics in Applied Mathematics – Computational Finance
(Spring 2007)
Home
page of the course at Rutgers University web site
University Academic Calendar
Quantitative Finance Software on the Web
Prof.
Paul
M. N. Feehan course 16:642:621
This page will record the topics we cover, with links and information on the related problem assignments and readings. Reading the material from the books on reserve books listed is strongly suggested, but not absolutely necessary. Reading the required text and handouts is required reading. The student should have read the material before coming to the class in which it is discussed!
Homeworks assignments
The homework assignment is given at the end of the lecture and usually is available online same day or even before at this page. The due for the assignment is the day of the next lecture. After a careful consideration I have decided to collect your work by email unless otherwise is clearly specified. Please, use aitkin@math.rutgers.edu for this purpose, and clearly indicate in the subject the assignament number.
Grading system
HW = 40%
Midterm exam = 30%
Final exam = 30%
Office hours
As I work in NYC the only suitable time for the office hours is Wednesday from 6 till 6:40 pm or in some cases after the lecture (after 9:40 pm). I apology for being not able to guarantee my presence exactly at 6 pm because of traffic. Also I could meet anybody, when in NYC, on Monday or Friday. Just send me email in advance.
This page will record the topics we cover, with links and information on the related problem assignments and readings. Reading the material from the books on reserve books listed is strongly suggested, but not absolutely necessary. Reading the required text and handouts is required reading. The student should have read the material before coming to the class in which it is discussed!
Notation:
QMDF
- Domingo Tavella, Quantitative Methods in Derivatives Pricing: An Introduction
to Computational Finance, Wiley 2002, ISBN 0471394475.
IDM - L. Clewlow and C. Strickland, Implementing Derivative Models, Wiley,
1998
MDC - J. London, Modeling Derivatives in C++, Wiley, 2004
FDMFE - D. J. Duffy, Finite Difference Methods in Financial Engineering : A Partial
Differential Equation Approach, Wiley, 2006
GL -
P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer,
2003
BM - D. Brigo, F. Mercurio Interest Rate Models - Theory and Practice: With Smile, Inflation
and Credit , Springer, 2006
Remember, slides and presentations at this page are provided only as an extra source, while the basic reading is given in the column "Reading".
|
Lecture |
Topics |
Reading |
Assignments |
|
1 |
- General
problems of computational finance - pricing, calibration, curve
fitting. (slides #1) |
QMDP, chapter
1,2 |
1. Homework
assignment 1 |
|
2 |
- Impied
trees, calibration to the smile (Mordecki
presentation), (Derman
paper) |
IDM, chapter
5 |
2. Homework
assignment 2 |
|
)3 |
- BS-wise
version of FFT |
Itkin's
presentation |
3. Homework
assignment 3 |
|
4 |
- Quasi-random numbers (1) |
QMDF - chapter 4 |
|
|
5 |
- Valuing European style
options with Monte Carlo. Reducing
the error in the estimate
(slides here
from slide 55) |
QMDF - chapter 5 |
4. Homework
assignment 4 |
|
6 |
- Introduction
to Finite difference method (1) |
QMDF - chapter 7 |
|
|
7 |
-
Coordinate
transformation (1) |
QMDF |
5. Homework
assignment 5 (deadline - 3/21) |
|
8 |
- Stability of finite-difference scheme
(1 from page 37, 2) |
QMDF - |
6. Homework
assignment 6 (deadline - 3/28) |
|
9 |
- ADI, method of lines (1) |
FDMFE -chapter 19, 20, 23, 27 |
7. Homework
assignment 7 (deadline - 4/5) |
|
10 |
- Variance
and Volatility Swaps. |
8. Homework
assignment 8 (deadline - 4/12) |
|
|
11 |
- Convertible bonds |
|
|
|
12 |
- How
to call C++ dll from Excel |
|
9. Homework
assignment 9 (deadline - 4/25) |
|
13 |
Interest rates models (site of Damiano Brigo) |
BM |
|
Below is a list of projects proposed for the final exam. The students could group together to fulfill the project, but the number of students on any one project is limited to 5. The students could list their choices in order of preference by March 18. After that the final assignment will be made. The students should write their own individual programs and submit individual reports. In orther words they can informally help each other, but overall we want to test individual effort.
The final exam period ends May 9 for this course and that is the last possible day, absolutely no exceptions whatsoever (short of the universe self-destructing), on which the students can turn in their project. Therefore I prefer an earlier deadline which is May 1, 2007.
The final project has to be submitted in the form of an essay. The projects should be well-structured and have the following key ingredients. To make it concrete, I'm illustrating with a typical example.
SAMPLE TOPIC: Finite Difference Solution to Heston Model
REPORT: This should have the following ingredients:
- *Must be written in LaTeX or similar scientific writing package.
- **Essay describes the underlying theory, numerical algorithms used, any special computational issues, numerical results and explanation.
- List of references must be included.
*Results section includes comparison of model with (a) market data, or (b) benchmark data (for example, published Heston option values for specific model parameters), or (c) exact solutions (for example, Heston closed-form), or (d) other models (for example, Black-Scholes), or (e) some other demonstration of code correctness.
**Results should be presented in tabular and graphical form.
CODE:
Matlab or C++ program allowed, so long as code runs (which whould be submitted). A complete C++ program can incorporate QuantLib or other classes, but must reference all sources in program comments, including code contributed by other students.
INDIVIDUAL EFFORT: Students working on the same topic can cooperate but must make documented individual effort. Evidence of copying without attribution will result in a score of zero for all students affected.
PROJECT GRADE: Based on the quality of the following key components:
- Theoretical model description.
- Results presentation, description, and explanation.
- Code, proportion of self-written versus adapted code, depth of new coding effort.
- Evidence of individual effort.
- Project level of difficulty (less progress on a challenging project is equivalent to more progress on a simpler project).
- The project description should include a strong statement that work submitted should primarily be the student's own and that all sources used (eg, Matlab, C++ code, papers, etc) be professionally cited and acknowledged.
TOPICS:
Topic 1, Topic 2, Topic 3, Topic 4, Topic 5
Links:
University Academic Calendar
Registrar's Class Roster (RCI login required)
RAMS mailing list management for math612_springl2007 (at) rams.rutgers.edu (RCI login required)
Instructor homepage
Teaching Assistant homepage
Library reserve list
Library (RCI login required for off-campus electronic journal access)
Quantitative finance software
Disclaimer: Posted for informational purposes only
This material is posted by the faculty of the Mathematics Department at Rutgers New Brunswick for informational purposes. While we try to maintain it, information may not be current or may not apply to individual sections. The authority for content, textbook, syllabus, and grading policy lies with the current instructor.
Information posted prior to the beginning of the semester is frequently tentative, or based on previous semesters. Textbooks should not be purchased until confirmed with the instructor. For generally reliable textbook information—with the exception of sections with an alphabetic code like H1 or T1, and topics courses (197,395,495)—see the textbook list.