Monte Carlo Methods in Finance

Prof. Dr. Alberto Suárez

Field/Discipline : Natural Sciences, Mathematics and Computer sciences

Language : There will be two versions of the course: [ENG] English and [ESP] bilingual Spanish - English (Videos in English with subtitles in Spanish. Additional documentation, exercises and quizzes in Spanish. Student interaction in both Spanish and English)

Institution : Universidad Autónoma de Madrid (Spain)

Course Description

In this course you will simulate prices of financial assets, use the Black-Scholes model to price European or Asian options, compute the Value-at-Risk of a bank and model financial time series with GARCH processes. The approach is hands-on with a strong emphasis on practical simulations that you will program, run and explore in your own computer.

"Monte Carlo methods in finance" will be offered on Iversity in the Fall semester 2013. The material is structured in 12 one-week units

Unit 1: Introduction and overview of the course
Unit 2: Generating random numbers
Unit 3: Generating simulations
Unit 4: The Black-Scholes model
Unit 5: Pricing of simple derivative products
Unit 6: Variance reduction techniques I
Unit 7: Pricing of exotic options
Unit 8: Variance reduction techniques II
Unit 9: Modeling of dependencies with copulas
Unit 10: Modeling and quantifying financial risk
Unit 11: Time series analysis and modeling
Unit 12: Advanced topics for further exploration

There will be two versions of the course:
[ENG] English

[ESP] bilingual Spanish - English
The videos are the same as in the English version and will be subtitled in Spanish. Additional documentation, exercises and quizzes will be in Spanish. There will be interaction among students and with the course tutors both in Spanish and in English.

Learning objectives

  1. Why are random numbers needed in quantitative finance? And, if they are random, how can they be used to give precise, accurate answers to quantitative financial problems?
  2. What is the Black-Sholes model and how can it be used to simulate the evolution of asset prices in financial markets?
  3. How are Monte Carlo methods used to determine the right price of a derivative product, such as a European call?
  4. What is the theory of copulas and how can it be used to model general dependencies among financial assets?
  5. How is financial risk modeled, characterized and quantified?

MOOC relevance

Courses in the area of quantitative finance are currently in high demand but are of difficult access. Furthermore, banks, insurance companies, utilities and financial firms need qualified professionals who understand both the financial and the computational issues that arise in the day-to-day activities of these institutions. Making this course available in an open online platform will allow thousands of students to acquire these qualifications, especially in regions where access to higher education is limited.

From our experience of more than 10 years teaching university-level courses in computational finance a programming approach based on simulation has proven a very successful way to make the material accessible to students of very different backgrounds (Mathematics, Physics, Engineering, Economics, Finance, Actuarial Sciences, etc.). Through the coding of programs and the design of simulations the students assimilate the material and develop their skills with relative ease, in spite of the difficulty of the financial and mathematical concepts involved. This interactive and constructive learning approach also boosts the students' confidence on their own skills and increases their satisfaction with the learning process.

Prior Knowledge

The course is geared to students not only in economics and finance, but also in mathematics, computer science, engineering, physics and the natural sciences.

No knowledge of finance is required.

Basic knowledge of Calculus (integration and differentiation, Taylor series), Linear Algebra (matrices, determinants, eigenvalues and eigenvectors) and Probability (random variables, probability density and cumulative distribution functions) at an introductory undergraduate level is recommended. Nevertheless, the students will have access to short videos and related exercises that introduce the mathematical concepts required for understanding each basic unit. Students familiar with these concepts can skip this material and focus on the main line of the course.

Programming knowledge is helpful but not a requirement. We will be designing simulations in Octave or in the R programming language. The programs will be short, intuitive, fully documented and easy to follow. Yet they will be powerful tools under the student's control, and will allow her to explore, experiment and learn at her own initiative.


  • Multiple Choice Test
  • P2P-grading of assignments
  • Discussions / Q&A

Additional tools

One of the goals of the course is that the students get to program their own simulations, so that they can understand, analyze and modify the conditions in which these simulations are run. For this purpose they will be programming in either GNU Octave [] or the R programming language []. Both are high-level languages for numerical and statistical computing that are available as free software. They are also easy to use even for students with limited or no programming experience.

Use of online-tools

First step: Develop your own code
Students will be required to develop their own programs by filling short portions of code with the key steps in the algorithms presented. In case that they do not succeed, the solutions will be available for them to use.

Second step: Run simulations
Students are expected to use the code developed to run simulations under different conditions. Precise and detail instructions will be given to the students so that they can modify the conditions of the simulations in a meaningful manner.

Third step: Learn from the analysis of the simulations performed.
A detailed analysis of the results will be made using the results of these simulations as a reference.


  1. Derivatives: The theory and Practice of Financial Engineering
    Paul Wilmott; John Wiley and Sons NY (1999)

  2. Monte Carlo Methods in Financial Engineering.
    P. Glasserman; Ed. Springer-Verlag, NY (2003)

  3. Options, Futures and other derivatives (8th Edition)
    J.C. Hull ; Prentice-Hall London (2011)


  5. Quantitative Risk Management
    A. J. McNeil and R. Frey, P. Embrechts

    Princeton Series in Finance, NY , (2005)

Prof. Dr. Alberto Suárez (Universidad Autónoma de Madrid (Spain))



Alberto Suárez received the degree of Licenciado in Chemistry from the Universidad Autónoma de Madrid, Spain, in 1988, and the Ph.D. degree in Physical Chemistry from the Massachusetts Institute of Technology (MIT), Cambridge, MA, in 1993. After holding postdoctoral positions at Stanford University (USA), at the Université Libre de Bruxelles (Belgium), as a research fellow financed by the European Commission within the program “Training and Mobility of Researchers”, and at the Katholieke Universiteit Leuven (Belgium), he is currently a professor in the Computer Science Department of the Universidad Autónoma de Madrid (Spain). He has also held appointments as “senior visiting scientist” at the International Computer Science Institute (Berkeley, CA) and at MIT (Cambridge, MA). He has worked on relaxation theory in condensed media, stochastic and thermodynamic theories of nonequilibrium systems, lattice-gas automata, and automatic induction from data. His current research interests include machine learning, quantitative and computational finance, time series analysis and information processing in the presence of noise.


Lorenzo Hernández, JorgeTejero, Alberto Suárez, Santiago Carrillo-Menéndez
"Percentiles of sums of heavy-tailed random variables: beyond the single-loss approximation"
Statistics and Computing [ISSN:0960-3174]
Vol. February, pp. 1-21 (2013)

Daniel Hernández-Lobato, Gonzalo Martínez-Muñoz, Alberto Suárez
How large should ensembles of classifiers be?
Pattern Recognition [ISSN: 0031-3203]
Vol. 46(5), pp.1323, 1336 (2013)

Alberto Suárez, Robert Silbey and Irwin Oppenheim
"Phase transition in the Jarzynski estimator of free energy differences"
Physical Review E [ISSN: 0031-9007 (print), 1079-7114 (online)]
Vol. 85 (5), pp. 051108-1,051108-13 (2012)

Jiahao Chen, Eric Hontz, Jeremy Moix, Matthew Welborn, Troy Van Voorhis, Alberto Suárez, Ramis Movassagh, and Alan Edelman
Error analysis of free-probability approximations to the density of states of disordered systems
Physical Review Letters [ISSN: 0031-9007 (print), 1079-7114 (online)]
Vol. 109(3), pp.036403-1, 036403-5 (2012)

Santiago Carrillo-Menéndez and Alberto Suárez
"Robust quantification of the exposure to operational risk: Bringing economic sense to economic capital"
Computers & Operations Research [ISSN: 0305-0548]
Vol. 39(4), pp. 792, 804 (2012)