Stochastics and Financial Mathematics

Model and quantify uncertainty

Stochastics and Financial Mathematics

Stochastics examines phenomena in which chance plays a central role, such as the result of a general election, fluctuations in share prices or the interactions between molecules in a living cell. If you opt for the Master’s programme in Stochastics and Financial Mathematics, you will be trained to become a world-class expert in both theory and relevant areas of application. The Master’s programme in Stochastics and Financial Mathematics at VU Amsterdam trains you in the full depth and breadth of the field, expanding your abilities and insights and enhancing your opportunities on the job market.

As a Stochastics and Financial Mathematics student at VU Amsterdam, you have a wide variety of courses to choose from, including all designated SFM courses offered by the two research universities in Amsterdam (UvA and VU) and the national Mastermath programme. Moreover, our department maintains close contact with many financial and other businesses that offer internship opportunities to carry out the concluding project of your Master's programme and get a head start on your career.

MSc Stochastics and Financial Mathematics in Amsterdam

The Master’s programme in Stochastics and Financial Mathematics is a two year programme, divided into four semesters. It consists of specialized courses, optional courses and seminars, and concludes with the Master’s Project, which usually takes the form of an external internship, but can also be a research project at our Department of Mathematics.

Courses
This programme focuses on phenomena in which chance plays a central role, such as election results, fluctuations in stock prices or complex networks in a living cell, with a specific focus on Financial Mathematics, an important field of application for stochastics.

Courses you can follow include Stochastic Processes for Finance, Interest Rate Models, Applied Stochastic Modelling, Optimization of Business Processes and Statistics for High-dimensional Data. Each semester you select four or five subjects from the list of recommended SFM courses. Of all the courses you choose, at least two must be Financial Mathematics courses, and at least two must be advanced SFM courses. See this minimanual for the full details of the programme.

In certain cases, and in consultation with our staff, you can substitute some of these SFM courses with other relevant mathematical modules, such as Partial Differential Equations or Functional Analysis. You can also choose courses from other disciplines, including Mathematics, Econometrics and Bioinformatics, allowing you to tailor your study path to your specific interests.

Our programme is offered in full collaboration with the University of Amsterdam (UvA). Thus, you benefit from the expertise, networks, partnership projects, and international reputation of both VU Amsterdam and UvA. Moreover, you can choose from a wide variety of courses, both from the local programmes of UvA and VU, and from the nationwide Mastermath programme, a combined effort of nine Dutch universities to organize courses in Mathematics of the highest quality that are open to students from all participating universities.

Master Seminar
During the entire first year, you will participate in the weekly Master Seminar. The seminar is led by active mathematicians who will introduce you to the local research groups in your field of specialization. You will also learn about possible thesis projects, practice giving advanced mathematical presentations, and experience what it means to be part of an active research community.

Master's Project
The last semester is dedicated to the Master’s Project. Most students in the Stochastics and Financial Mathematics programme choose to do an external internship at a company or research facility as their Master's Project. During this internship you will work under supervision of an advisor from the company and a staff member from the Department of Mathematics. VU Amsterdam maintains close contact with many financial and other businesses, offering plenty of internship possibilities.

As an alternative, your Master's Project can also take the form of a research project carried out under the supervision of one of our staff members. See Current research topics below for an impression of the kind of topics you can address in your Master's Project.

All Master's Projects are completed by writing a thesis and presenting your results in a colloquium.

More information
For more information on internships and work placement opportunities, you can consult the website of the Internship Office for Mathematics and Computer Science. Further information about the Master’s programme in Stochastics and Financial Mathematics and descriptions of course modules can be found in the study guide.

How fast can a Bayesian procedure learn an unknown function?
In many settings data is used to determine an unknown response curve, probability density or regression surface. One method is to model such a function a-priori as a sample path of a Gaussian or other process and reconstruct it by Bayes' rule. Does this work? Can one express the precision of the procedure in terms of the amount of information in the data?

Valuation and hedging of derivatives
As a Master student, you can study the pricing of exotic options in equity or fixed income, as well as hybrid constructions in a model or a model-free context. Alternatively, you can investigate stochastic volatility models or arbitrage-free models for the term structure of interest rates. Developing the underlying mathematical tools and concepts needed in finance (involving areas like stochastic analysis, Levy processes, complex analysis or PDEs) can also be the topic of a Master's Project.

Credit crisis
Analysing the risks associated with financial assets is at least as important as analysing their yields. The credit crisis has made that painfully clear. How can statistical and probabilistic methods contribute to the risk management procedures at financial institutions?

Keeping pension funds healthy
The declining performance of the stock market and the declining interest rates in the last decade pose a major challenge to pension funds. Stochastic models are used intensively to analyse the market and to propose appropriate policy adjustments to ensure future growth.

Signal detection: a needle in a haystack
Finding the genes responsible for complex diseases in the analysis of gene expression data is like looking for a needle in a haystack. Thorough statistical and computational methods are essential for separating signal from noise in experimental and population data.

Discovering structures in high-dimensional data
The need of methods for intelligent processing of data is rapidly growing with the increasing accumulation of data sets of often very high dimension and size. Unsupervised exploratory analysis plays an important role in the study of large, high-dimensional datasets that arise in a variety of applications. Broadly speaking, the goal of such analysis is to find structures or patterns in the data.

Multiple comparison problems
When testing a single hypothesis, one is usually concerned with controlling the false positive rate while maximizing the probability of detecting the effect (in statistical terms: maximize the power conditional on the Type I error being at or below some level). Multiple testing problem refers to the testing of more than one hypothesis at a time. Modern scientific technologies are providing a new class of large-scale simultaneous inference problems, where one needs to conduct massive multiple comparisons, for example, in the analysis of gene expression data.

We offer a special programme in Stochastics and Financial Mathematics for outstanding students from our partner universities. The short track programme consists of one full year of study. You should be able to obtain at least 66 EC in courses (30 EC) and a Master’s Project (36 EC) in this one year.

Application for this programme is possible if you have finished at least 60 EC of courses at Master's level at one of our partner universities that entitle you to exemptions for Master's courses at VU Amsterdam.


Students from our partner universities are encouraged to opt for this programme through their respective contact persons:

Partner universityContact person
Eötvös Loránd University (Budapest, Hungary)Prof. G. Michaletzky
University of Warsaw (Warsaw, Poland)Prof. Agnieszka Bojanowska empty
Jagiellonian University (Krakow, Poland)Prof. K. Ciesielski
Charles University (Prague, Czech Republic)please contact: admissionsfs@vu.nl 
University of Silesia (Katowice, Poland)Dr Michał Baczyński
Comenius University (Bratislava, Slovakia)Prof. dr. Marek Fila


Admission and application

The Examination Board of the Faculty of Sciences will decide which applicants will be admitted to the Short track Master's programme in Stochastics and Financial Mathematics, and will also evaluate requests for course exemptions.

  • Please note that you can only apply for the Short Track Master's programme if you are a student from one of the above mentioned partner universities!
  • Contact your coordinator to discuss your study plans. You need a formal approval from your coordinator that you are selected for the Short Track Master. We will be informed by your coordinator if you have been selected.
  • Apply online as described here. Please note that you will not find the option 'Short Track Master' in Studielink, so just select the regular master's programme of your choice. The application deadline is 1st of April. However, if you also would like to apply for the VU Fellowship Programme (VUFP), you should send in both applications before 1st of March.
  • You will have to upload a set of documents for your online application. If you have any questions about the requested documents, please contact the International Office. Please start your application, even if you cannot provide all documents.
  • Send the following documents (also) by regular mail to:  

    VU Amsterdam 
    International Office/Degree Mobility Unit  
    De Boelelaan 1105 
    1081 HV Amsterdam 
    The Netherlands 

    1. A completed application form signed by a senior faculty representative at your home university. Please mention your VU student number (which you will receive once you have started your online application); 
    2. Your CV / Resume in English; 
    3. A form with list of completed courses (transcript of records) ttaken at your home university and a list of courses that you still intend to take at your home university. Please have these lists signed by a faculty representative from your home university; 
    4. Recommendation letters from a senior member of your faculty (a professor in your department).

Scholarships
Information on possibilities of financial aid can be found here.

More information
For practical matters, like accommodation, living costs, financial aid, work, etc., please contact our International Office: admissionsfs@vu.nl.

A Master's degree in Stochastics and Financial Mathematics will be a great asset to you in finding employment in the business world, especially with major financial institutions. Employers may be:

  • Banks 
  • Insurance companies 
  • Actuarial consultancies 
  • Forensic institutes 
  • Statistical or planning agencies 
  • Railway companies 
  • Telecommunications companies

Many students embark on a career path in which they do not only use their mathematical background, but also benefit from the personal and organizational skills developed in the programme.

Continuing your studies

You may also choose to continue your studies after graduation. Candidates with excellent grades can apply for one of our PhD student positions. These are normally awarded for four years, during which you are expected to complete a research project.

Located near the financial heart of Amsterdam
We are located at the Zuidas campus in Amsterdam, at a stone's throw from the financial heart of Amsterdam. Our department maintains close ties with companies in the financial epicentre of the Netherlands. The VU campus is very well connected by public transport to the inner city of Amsterdam, Schiphol international airport, and the rest of the Netherlands.

Outstanding research
The Department of Mathematics at VU Amsterdam is a top-ranked training and research institute. The Netherlands Organization for Scientific Research (NWO) regularly awards VENI, VIDI and VICI grants for innovative research to researchers at VU Amsterdam.

Individual attention
The Master’s programme in Stochastics and Financial Mathematics is a small-scale programme that is characterized by a personal style with individual attention, and where student-teacher interaction plays a key role. Students benefit from having the opportunity to study in small groups and work closely together with the academic staff.

Collaboration and nationwide courses
The Stochastics and Financial Mathematics programme is offered in full collaboration with the University of Amsterdam (UvA). Thus, you benefit from the expertise, networks, partnership projects, and international reputation of both VU Amsterdam and UvA.

Moreover, the Departments of Mathematics of nine Dutch universities have combined their efforts by offering courses open to all Master's students in Mathematics. This Mastermath initiative offers students the highest quality of instruction and opens opportunities for interaction with students from other mathematics institutes. The joint courses widen the options for students who intend to pursue a PhD programme after completing their Master's programme. As a student in the Stochastics and Financial Mathematics programme you will also be following Mastermath courses.

Student experiences

Floris
"Before starting the Master's programme in Stochastics and Financial Mathematics I studied Econometrics, also at VU Amsterdam. The SFM Master seemed like a nice bridge to study the same concepts I studied in Econometrics in a more rigorous way. During my Master's I focused mainly on the tochastics track, eventually writing my thesis on a geometric approach to Maximum Likelihood estimators. The programme itself imposes very little restrictions on its contents, and I really enjoyed having the freedom to choose courses that helped me obtain the more rigorous understanding of statistical concepts I was looking for. Currently I apply these concepts on a daily basis in my work as a Data Scientist."

Daniel Krycha

"During my Master‘s studies in Prague I focused on stochastic modeling of interest rates, which is why the programme Stochastics and Financial Mathematics sparkled my interest. The short track version of the programme offered by the Vrije Universiteit Amsterdam was especially attractive for me, as it allowed me to use the erudition I had already gained to develop modern specialisations in my field of interest.

The unique thing about the programme is that it unites lectures offered by four science faculties, each of them belonging to a Dutch university ranked within top 200 universities in the world. The very personal approach of the teachers without any formal hierarchy ensures that you build close relationships with them and you will find assistance in your day-to-day issues, whether you struggle with administrative technicalities or you are looking for supplementary literature.

The true student life experience is then completed with the inspiring athmosphere of Amsterdam, famous for its numerous study associations, extensive cultural and sports opportunities, and the welcoming nature towards international community. If you decide to stay after your studies, you can expect a broad range of career opportunities. 

Daniel Krýcha, Czech Republic

Anna

“I was a Short Track Master student in Stochastics and Financial Mathematics. Before that I had studied Mathematics at University of Warsaw. I was mostly interested in probability theory and its applications, that is why I chose this programme at VU Amsterdam. It offers a wide range of subjects, both theoretical as well as more practical ones. Since I already had an academic background, I focused on applications, for example in genetics, queuing systems or simulation methods.

For me, as an international student, studying in Amsterdam was very interesting not only for academic reasons. I could experience life in a multicultural environment and I met many people from different parts of the world. In addition, the city of Amsterdam is certainly a great attraction itself. I can say that I fully enjoyed this one year at VU Amsterdam.”

Anna Aksamit, Poland

Lenka

“The short track Master’s programme Stochastic and Financial Mathematics was a great opportunity for me. After I finished my first year of master studies in Econometrics at my home university in Czech Republic, I decided to take the chance and study at the VU Amsterdam. 

The programme itself is perfectly organized and of a high quality. One can choose from a huge variety of stochastics classes, ranging from basic theory of mathematical statistics and probability to much more advanced and interesting classes from the field of mathematical finance. I decided to focus on the financial classes, as the stochastic modeling in finance is of rising importance in the business world. Modeling and forecasting of interest rates, stock prices, pricing of financial derivatives etc. became the main topic of risk management in banks.  And a highly qualified quant analyst is the one for such a job.”

Lenka Slamova, Czech Republic

Rick

“After obtaining my Bachelor's degree in Mathematics from VU Amsterdam, I opted for the Master's in Stochastics and Financial Mathematics because I wanted to move into finance: shares, indices, prices, options and so on. Stochastics and Financial Mathematics is a well-structured programme; you learn the theory first – the formulas and background – and only later apply that knowledge in practice.

The advantage of this programme is its small scale. You have a lot of contact with your fellow students, and with tutors who provide great supervision during your studies. And the advantage of VU Amsterdam itself is that all the courses are grouped together on one campus. That means that you can choose subjects from other courses, like Economics or Business Mathematics and Informatics, without having to travel to study them.

After my graduation I started working as a Risk Manager for Fortis Bank Nederland Clearing and Custody. This means I’m responsible for the model which is used for calculating the market risk of client portfolios. Due to changing market conditions we constantly have to update our model in order to improve the service towards our clients. Whenever one of our clients decides to trade in a new product, we have to come up with the correct theoretical valuation model which computes realistic risk numbers. It took me about half a year to get acquainted to the language of banking but the knowledge obtained during my studies helped me along the road.”

Rick Duursma, the Netherlands

Overview Stochastics & Financial Mathematics

LANGUAGE OF INSTRUCTION

English

DURATION

2 years

TUITION FEE

APPLICATION DEADLINE

1 June for Dutch students. 1 April for EU/EEA and non-EU/EEA students.*
* EU/EEA students with an international degree who do not need housing services through VU Amsterdam can still apply until 1 June.

START DATE

1 September
1 February

STUDY TYPE

Full-time

FIELD OF INTEREST

Computer Science, Mathematics and Business

Dutch students

Direct admission to the Master's programme in Stochastics and Financial Mathematics is possible with a Bachelor's degree in Mathematics or Technical Mathematics, or (with sufficient mathematical content) in Business Analytics, Econometrics or Actuarial Sciences from a university in the Netherlands. If you have a Bachelor's degree in another subject from a university or institute of higher education in The Netherlands or elsewhere, you require the approval of the Examination Board. The main admission criteria are:

- A Bachelor of Science.
- 90 EC (European Credit points) or equivalent of Mathematics courses at the BSc level, with a level of stochastics courses equivalent to that of the VU Bachelor's programme in Mathematics.
- English language skills at the level of TOEFL score 580 or above (only for students with a HBO degree).

For more details, please consult the Teaching and Examination Regulations for the Stochastics and Financial Mathematics Master's programme.


Entrants from higher vocational education (HBO) generally have to follow a large part of the Bachelor's programme before they can be admitted to the Master's programme in Stochastics and Financial Mathematics. Please contact the programme coordinator for more information.

Information about the programme

For further information about admission to the programme you can contact the master coordinator:

VU Amsterdam
Faculty of Sciences
Dr. Corrie Quant
De Boelelaan 1081
1081 HV Amsterdam
T +31 (0)20 598 7831
E c.m.quant@vu.nl

General information about VU Amsterdam

Please phone us at +31 (0)20 598 5000 (Monday – Friday, 10:00 to 12:00). You may also email us at study@vu.nl

Would you like to read the key points of the Master's programme? Order the brochure.

International students

Direct admission to the Master's programme in Stochastics and Financial Mathematics is possible with a Bachelor's degree in Mathematics, Engineering Mathematics, or Technical Mathematics from a University in the Netherlands. If you have a Bachelor's degree in another subject from a university or institute of higher education in The Netherlands or elsewhere, you require the approval of the Examination Board. The main admission criteria are:

 
- A Bachelor of Science.
- 90 EC (European Credit points) or equivalent of Mathematics courses at the BSc level, with a level of stochastics courses equivalent to that of the VU Bachelor's programme in Mathematics.
- English language skills at the level of TOEFL score 580 or above.

For more details, please consult the Teaching and Examination Regulations for the Stochastics and Financial Mathematics Master's programme.


General language proficiency requirements
VU Amsterdam requires international applicants to take an English test and to submit their score as part of the application. Exceptions are made for students who have completed their education in Canada, USA, UK, Ireland, New Zealand or Australia, or who have obtained an international Baccalaureate or European Baccalaureate diploma. Please check out the admission and language requirements for international students for more details.

There are several possibilities for obtaining funding. VU Amsterdam, the Dutch governement and other organisations offer scholarships, fellowships and grants

Information about the programme

For further information about admission to the programme you can contact the master coordinator:

VU Amsterdam
Faculty of Sciences
Dr. Corrie Quant
De Boelelaan 1081
1081 HV Amsterdam
T +31 (0)20 598 7831
E c.m.quant@vu.nl

Practical information for international students

Would you like to know more about our courses, scholarships and application & registration procedure? Please contact our International Office.

Email: admissionsfs@vu.nl

General information about VU Amsterdam

Please phone us at +31 (0)20 598 5000 (Monday – Friday, 9:00 to 12:00). You may also email us at study@vu.nl

Would you like to read the key points of the Master's programme? Order the brochure.