FE621 Computational Methods in Finance
Course Catalog Description
Introduction
The main goal of a student enrolled in FE621 is to obtain essential computational tools used in the financial industry by modern financial quantitative analysts. The students are to become familiar with such methods as stochastic processes approximation, an approximation for solutions to PDE’s, decision methods, and simulation. The purpose is to learn to apply the results 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).
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.
Campus  Fall  Spring  Summer 

On Campus  X  X  
Web Campus  X  X  X 
Instructors
Professor  Office  

Ionut Florescu

ionut.florescu@stevens.edu  Babbio 544 
Course Resources
Textbook
We will not have a single required textbook in this class. Such a textbook has not been written yet. However we shall be using chapters, parts, and examples from the following textbooks. The books that are most heavily used are noted below.
 AB: Aichinger, Michael and Adnreas Binder. “A Workout in Computational Finance”. John Wiley & Sons, 2013. (light use  easy to read)
 CS: Clewlow, Les, and Chris Strickland. “Implementing Deriva tive Models (Wiley Series in Financial Engineering).” (1996). (we will use this text heavily: rank 1)
 FR: Fusai, Gianluca, and Andrea Roncoroni. “Implementing Models in Quantitative Finance: Method and Cases”. Springer , 2007. (moderate use: rank 2)
 R: Rouah, Fabrice D. “The Heston Model and its Extensions in Matlab and C#”. John Wiley & Sons, 2013. (moderate use: rank 3)
Additional References
 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).
 Assignments require knowledge of one of the following programming 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 programming languages.
Grading
Grading Policies
 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 is to use a pdf printer driver. I write all my documents in LATEX, and that typesetting program produces pdf files. A simple alternative (using any typesetting program) would be to 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 me before you fall behind.
 Generally the grade distribution follows the following percentages.
 Assignments 30%
 Midterm 25%
 Final 40%
 Quizzes, class participation 5%
Lecture Outline
Topic  Reading  

Week 1 and Week 2  Intro., Review BlackScholes model,
Heston and SABR models, Finding zeros of functions, Greeks and Quadrature methods 
Notes, AB1, CS1
R1, 2 F15.1 CS1, R11, F6 
Week 3 and Week 4 
Tree approximating methods,
Binomial Tree Model, Trinomial Tree Model and extensions 
AB2, 4
CS2,3 
Week 5 to Week 7 
PDE approximation methods
Finite difference methods Finite element methods Exercise frontier for American options 
AB3, 7, CS 3, 5
FR4, 5.4,15,17 R8, 10 
Week 8 
PDE Transformation methods
Laplace, Fourier methods, Heston model 
AB12, FR7, R4,5 
Week 9  MIDTERM  
Week 10  Optimization and parameter calibration  AB15,16 FR24,25, R6 
Week 11
Week 12 
Path approximation methods
Random number generation Univariate Monte Carlo methods Cholesky decomposition Multivariate Monte Carlo, Variance reduction Markov Chain Monte Carlo (MCMC) 
Notes, AB9,11, CS4
FR1,2, R7 AB8,10 FR13,14, R7 
Week 13
Week 14 
Multivariate Stochastic processes
PCA and Factor models Copula modeling. Application to CDO 
AB17.2, CS p. 128, FR22,23
AB14, FR8, 22 
Week 14  Week 14 topic is going to be presented if time permits. 