FE621 Computational Methods in Finance

Course Catalog Description


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 has three main pillars centered around computational methods for pricing and hedging of derivative securities (additional topics will be covered as time permits):

  1. Review of stochastic calculus and risk-neutral pricing
  2. Pricing based on lattice/tree methods
  3. Pricing based on Monte Carlo simulation
  4. Finite difference methods for PDEs
  5. Other topics as time permits (transform methods, jump models, optimization/calibration, PCA, factor models, applications in risk management, high frequency trading,…)

Campus Fall Spring Summer
On Campus X X
Web Campus X X X


Professor Email Office
Sveinn Olafsson solafsso@stevens.edu

Course Resources

Course Materials

Class notes will be posted on Canvas. The topics covered can be found in a variety of textbooks and other online sources, such as

  1. L. Clewlow and C. Strickland. Implementing derivative models, Wiley, 1998
  2. P. Glasserman. Monte Carlo methods in financial engineering, Springer, 2003.
  3. A. Hirsa. Computational methods in finance, Chapman & Hall, 2012.
  4. M. Mariani and I. Florescu. Quantitative Finance, John Wiley & Sons, 2019
  5. J. Hull. Options, futures, and other derivatives, Prentice Hall, 2014


Grading Policies

The course grade will be determined in the following manner:

  • 90% Homework assignments
  • 10% Class participation
Homework Assignments:
  1. There will be at least five individual homework assignments
  2. Assignments may have both a theoretical and a computational component
  3. You have 7 “late days” over the semester. Beyond that, late homework will not be accepted without prior notice and permission of instructor
  4. Homework should be submitted through Canvas as a single pdf file with name “hwNumber_LastName_FirstName.pdf”. For example: “hw1_Olafsson_Sveinn.pdf”
Important homework solution guidelines:
  1. Make an effort to present your homework solutions in a clear and readable manne
  2. Remember to explain your reasoning (correct answers from unjustified arguments are not correct solutions)
  3. In general, all code can go into an appendix
  4. You are welcome to discuss homework problems with other students, but you must write and submit and understand your own solution
  5. You are not allowed to consult with or use solutions of former students, or “mindlessly” copying/pasting from online sources. This will be considered as academic dishonesty.

Lecture Outline

Topic Reading
Week 1 and Week 2 Intro., Review Black-Scholes model,
Heston and SABR models,
Finding zeros of functions,
Greeks and Quadrature methods
Notes, AB-1, CS-1
R-1, 2
CS-1, R-11, F-6
Week 3 and Week 4 Tree approximating methods,
Binomial Tree Model,
Trinomial Tree Model and extensions
AB-2, 4
Week 5 to Week 7 PDE approximation methods
Finite difference methods
Finite element methods
Exercise frontier for American options
AB-3, 7, CS 3, 5
FR-4, 5.4,15,17
R-8, 10
Week 8 PDE Transformation methods
Laplace, Fourier methods, Heston model
AB-12, FR-7, R-4,5
Week 10 Optimization and parameter calibration AB-15,16 FR-24,25, R-6
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, AB-9,11, CS-4
FR-1,2, R-7
AB-8,10 FR-13,14, R-7
Week 13
Week 14
Multivariate Stochastic processes
PCA and Factor models
Copula modeling. Application to CDO
AB-17.2, CS p. 128, FR-22,23
AB-14, FR-8, 22
Week 14 Week 14 topic is going to be presented if time permits.