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FE 621A and WS Computational
Methods in Finance
Course objective
The main goal of a student enrolled in FE621 is to obtain essential compu-
tational tools used in the financial industry by modern financial quantita-
tive analysts. The students are to become familiar with such methods as
stochastic processes approximation, approximation for solutions to PDE’s,
decision methods, and simulation. The purpose is to learn to apply the re-
sults to forecasting, asset pricing, hedging, risk assessment, as well as other
financial problems. Students must have a strong mathematical background
(FE543/FE610), and be familiar with derivatives terminology and concepts
at the level of Hull’s textbook (FE620).
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The course is split in modules and each module will cover theory and test
the student’s knowledge on developing and implementing algorithms to solve
real problems.
Required material the following is the textbook for the class.
MF : Mariani, Maria C. and Ionut Florescu. “Quantitative Finance”,
John Wiley & Sons, ISBN-13: 978-1118629956 ISBN-10: 1118629957,
November 8, 2019.
We may be using chapters, parts, and examples from other books and
research articles. The books that have been used in the past are:
(a) CS: Clewlow, Les, and Chris Strickland. “Implementing Deriva-
tive Models (Wiley Series in Financial Engineering).” (1996).
(Please refer to this book for pseudocode)
(b) AB: Aichinger, Michael and Adnreas Binder. “A Workout in
Computational Finance”. John Wiley & Sons, 2013. (light use -
easy to read)
(c) FR Fusai, Gianluca, and Andrea Roncoroni. “Implementing
Models in Quantitative Finance: Method and Cases”. Springer ,
2007. (moderate use)
(d) R Rouah, Fabrice D. “The Heston Model and its Extensions in
Matlab and C#”. John Wiley & Sons, 2013. (moderate use)
(e) Recommended reading Options, Futures and Other Derivatives,
by John C. Hull, Prentice Hall, 2014, 9th edition, ISBN: 0133456315
(you may get any of the older editions as the current edition is
quite expensive. Use whatever edition you used in FE620).
(f) Assignments require knowledge of one of the following program-
ming languages: C++/C#, Java. You can use Matlab or R or
SAS or any computational language you wish. Please see the lab
courses offerings for introduction and refresher in these program-
ming languages.
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Grades – Please submit ALL the work using
pdf format
The final grade will be determined upon the student’s performance in the
course. We will have multiple assignments and quizzes throughout the course.
Most of the grade will be coming from the in class midterm as well as from
the final. The work tends to be programming intensive so an early start is
necessary especially if there are gaps in your programming skills.
Only use the .pdf format for submitting assignment files. You should be
able to transform any document into a pdf file. You can use Adobe acrobat
- should be free to Stevens students as far as I know (please call the students
help desk), or a simple alternative: use a pdf printer driver. I write all
my documents in LATEXand that typesetting program produces pdf files. A
simple alternative (using any typesetting program): search on google for a
driver that would print to a pdf file. Such drivers are generally free.
Late assignments will not be accepted under any circumstances without
prior notice and permission of the instructor. If outside circumstances are
affecting your ability to perform in the course, you must contact your in-
structor before you fall behind. It is recommended to notify at least 24
hours before due.
Generally the grade distribution follows the following percentages.
Table 1: Grade distribution
Assignments 30%
Midterm 25%
Final 40%
Quizzes, class participation 5%
Communication and lectures
This is the syllabus for the web versions of the FE621 class. Material and
notes may be posted on Canvas ahead of time, please read them ahead of
the respective class. Please see the tentative schedule posted at the end of
this document.
Students are encouraged to ask questions in class and post questions in
the discussion group/forum on the web site. In general, this encourages
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students to exchange ideas, view points on issues related to assignments and
projects. Active participation will be rewarded with bonus points. Posting
solutions is not appropriate but discussing the main points of the problems
is.
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Schedule
Week Material Reference Author-
Chapter.Section
Week 1 Intro., Quadrature methods, MLE, MF-1,2 CS-1
and Put/Call parity, Hedging AB-1, R-1,2
Week 2 Black Scholes, Heston and SABR models MF-3, CS-1
Implied vol, local vol, Bisection methods F-15.1, R-11, F-6
Tree approximating methods
Week 3 Binomial Tree Model MF-6, CS-2
Week 4 Trinomial Tree Model and extensions MF-6, CS-3 AB-2, 4
PDE approximation methods
Week 5 Finite difference methods MF 4.2,7.1-7.5, CS 3,5
Week 6 Finite difference method for Heston MF 7.6-7.7, R-11
Week 7 Approximating American options MF 7.8-7.9 R-8,10
PDE Transformation methods
Week 8 Laplace, Fourier methods, Heston model MF 4.4-4.6, 5 FR-7
Week 9 MIDTERM
Week 10 Optimization and parameter calibration MF-1.10, 9.6
Path approximation methods
Week 11 Random number generation MF 8.1-8.4, CS-4
Univariate Monte Carlo methods FR-1,2, R-7
Week 12 Cholesky decomposition MF 8.5-8.10
Multivariate Monte Carlo, Variance reduction FR-13,14, R-7
Markov Chain Monte Carlo (MCMC)
Multivariate Stochastic processes
Week 13 PCA and Factor models MF-16
Week 14 TBD and review TBD
ACADEMIC INTEGRITY
Graduate Student Code of Academic Integrity All Stevens graduate
students promise to be fully truthful and avoid dishonesty, fraud, misrep-
resentation, and deceit of any type in relation to their academic work. A
students submission of work for academic credit indicates that the work is
the student’s own. All outside assistance must be acknowledged. Any student
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who violates this code or who knowingly assists another student in violating
this code shall be subject to discipline.
All graduate students are bound to the Graduate Student Code of Aca-
demic Integrity by enrollment in graduate coursework at Stevens. It is the re-
sponsibility of each graduate student to understand and adhere to the Grad-
uate Student Code of Academic Integrity. More information including types
of violations, the process for handling perceived violations, and types of sanc-
tions can be found at https://www.stevens.edu/sites/stevens edu/files/Graduate-
Student-Code-Academic-Integrity.pdf.
Special Provisions for Undergraduate Students in 500-level Courses
The general provisions of the Stevens Honor System do not apply fully to
graduate courses, 500 level or otherwise. Any student who wishes to report
an undergraduate for a violation in a 500-level course shall submit the report
to the Honor Board following the protocol for undergraduate courses, and an
investigation will be conducted following the same process for an appeal on
false accusation described in Section 8.04 of the Bylaws of the Honor System.
Any student who wishes to report a graduate student may submit the report
to the Dean of Graduate Academics or to the Honor Board, who will refer
the report to the Dean. The Honor Board Chairman will give the Dean of
Graduate Academics weekly updates on the progress of any casework relating
to 500-level courses. For more information about the scope, penalties, and
procedures pertaining to undergraduate students in 500-level courses, see
Section 9 of the Bylaws of the Honor System document, located on the Honor
Board website.
Learning Accommodations
Stevens Institute of Technology is dedicated to providing appropriate accom-
modations to students with documented disabilities. The Office of Disability
Services (ODS) works with undergraduate and graduate students with learn-
ing disabilities, attention deficit-hyperactivity disorders, physical disabilities,
sensory impairments, psychiatric disorders, and other such disabilities in or-
der to help students achieve their academic and personal potential. They
facilitate equal access to the educational programs and opportunities offered
at Stevens and coordinate reasonable accommodations for eligible students.
These services are designed to encourage independence and self-advocacy
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with support from the ODS staff. The ODS staff will facilitate the provision
of accommodations on a case-by-case basis.
For more information about Disability Services and the process to receive
accommodations, visit https://www.stevens.edu/office-disability-services. If
you have any questions please contact: Phillip Gehman, the Director of Dis-
ability Services Coordinator at Stevens Institute of Technology at mailto:
[email protected] or by phone 201-216-3748.
Disability Services Confidentiality Policy Student Disability Files are
kept separate from academic files and are stored in a secure location within
the Office of Disability Services. The Family Educational Rights Privacy Act
(FERPA, 20 U.S.C. 1232g; 34CFR, Part 99) regulates disclosure of disability
documentation and records maintained by Stevens Disability Services. Ac-
cording to this act, prior written consent by the student is required before
our Disability Services office may release disability documentation or records
to anyone. An exception is made in unusual circumstances, such as the case
of health and safety emergencies.
Inclusivity
Name and Pronoun Usage As this course includes group work and class
discussion, it is vitally important for us to create an educational environment
of inclusion and mutual respect. This includes the ability for all students to
have their chosen gender pronoun(s) and chosen name affirmed. If the class
roster does not align with your name and/or pronouns, please inform the
instructor of the necessary changes.
Inclusion Statement Stevens Institute of Technology believes that diver-
sity and inclusiveness are essential to excellence in academic discourse and
innovation. In this class, the perspective of people of all races, ethnicities,
gender expressions and gender identities, religions, sexual orientations, dis-
abilities, socioeconomic backgrounds, and nationalities will be respected and
viewed as a resource and benefit throughout the semester. Suggestions to fur-
ther diversify class materials and assignments are encouraged. If any course
meetings conflict with your religious events, please do not hesitate to reach
out to your instructor to make alternative arrangements.
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You are expected to treat your instructor and all other participants in
the course with courtesy and respect. Disrespectful conduct and harassing
statements will not be tolerated and may result in disciplinary actions.
Mental Health Resources
Part of being successful in the classroom involves a focus on your whole self,
including your mental health. While you are at Stevens, there are many
resources to promote and support mental health. The Office of Counseling
and Psychological Services (CAPS) offers free and confidential services to
all enrolled students who are struggling to cope with personal issues (e.g.,
difficulty adjusting to college or trouble managing stress) or psychological dif-
ficulties (e.g., anxiety and depression) and who can visit the office in person.
CAPS is open from 9:00 am to 5:00 pm Mondays, Wednesdays, Thursdays
and Fridays and from 9:00 am to 7:00 pm on Tuesdays during the Fall and
Spring semesters; appointments are highly encouraged. For those students
who cannot visit the Stevens campus for an in-person appointment, you can
contact a local mental health care provider for an in-person appointment, or
if you are enrolled in the Stevens Student Health Insurance, you may call
Care Connect for 24/7 mental health support at 1-888-857-5462.
For further information please visit the CAPS webpage on Seeking Help
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