Financial Mathematics

Course manual 2025/2026

Course content

We will obtain insight into the mathematical structure of financial products such as futures, options and other derivatives. We will both deal with the discrete (Cox, Ross and Rubinstein) and continuous models (Black and Scholes).  We will also treat time series models. Attention will be given to the role of volatility in financial processes. In an extended case study both option theory and times series analysis will be studied throughout the course. The course is both theoretical and practical and aims to give a broad view of the field of financial mathematics.

Study materials

Literature

• J.Hull, 'Options, Futures, and Other Derivatives'

• Etheridge, 'A Course in Financial Calculus'

Software

• Python (or alternatives)

Objectives

• The student understands at the end of the course the working of financial markets from a technical view point.
• The student understands the working of basic models to value options and other derivatives in detail (i.e. Cox, Ross and Rubenstein and Black and Scholes).
• The student understands the role of arbitrage in financial processes.
• The student understands Ito's lemma.
• The student understands Call and put options as well as the Greeks.
• The student understands the role of stochastics in financial processes.
• The student understands basic risk models and popular time-series models.
• The student knows what volatility means in a detailed fashion.

Teaching methods

• Hoorcollege
• Werkcollege
• Computer lab session/practical training
• Lecture
• Seminar

The theory is explained at the plenary sessions. Here the structure of the theory is revealed and it is shown what the underlying ideas are.  During the practical classes the assignments will be discussed and students will be helped with completing their homework.

Learning activities

Attendance

Attendance requirements for the program (OER - Part B):

• Active participation is expected from every student in the course component for which the student is enrolled.
• In addition to the general requirement that the student actively participates in the education, the additional requirements per component are described in the study guide. It also specifies which parts of the component have a mandatory attendance requirement.
• If a student is unable to attend a mandatory part of the program due to personal circumstances, the student must report this in writing as soon as possible to the relevant lecturer and the study advisor.
• It is not permitted to miss mandatory parts of a component if there are no personal circumstances.
• In cases of qualitatively or quantitatively insufficient participation, the examiner may exclude the student from further participation in the component or part of it. Conditions for sufficient participation are determined in advance in the study guide and on Canvas.

Assessment

Inspection of assessed work

Contact the course coordinator to make an appointment for inspection.

Assignments

Weekly homework. Counts towards 30% of final grade.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Additional information

Recommended prerequisites: Measure Theory.

Contact information

Coordinator

• dr. Robin de Vilder

lecture: Dr. Robin de Vilder (r.g.devilder@uva.nl)

exercise classes: Dr. Mike Derksen (m.j.m.derksen@uva.nl)