Inleiding financiele wiskunde (2025/2026: Periode 2)

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Cursusdoel

Zie onder vakinhoud.

Vakinhoudelijk

This is a course on Brownian motion, Ito calculus and its application to financial mathematics. The course is designed for students with a background in probability (BSc Mathematics level) and an exposure to bachelor level measure theory and stochastic processes. We start with a review of all the necessary background, then move to the concept of Brownian motion and discuss some of its important properties like quadratic variation and the Markov property. We then discuss stochastic calculus, in particular the Ito-Doeblin formula and the derivation of the Black-Scholes-Merton formula for pricing European options. After making this link with financial mathematics, we introduce risk-neutral pricing and discuss Girsanov's Theorem and Fundamental Theorems of Asset Pricing. We (start and) end the course, with a discussion of financial options, option trading and the relevant mathematical concepts in practice.
This course is one of the modelling courses in the bachelor programme with major 'mathematics' or 'mathematics and applications'. Please find more information on the students website.

Learning goals:
At the end of this course, the student
  • has an in-depth knowledge of Brownian motion, their essential properties
  • has in-depth knowledge in Ito-Calculus, in particular the Ito-Doeblin Formula
  • has an understanding of the derivation and the application of Black and Scholes formula in Financial Mathematics
  • ​has the knowledge and usage of the risk-neutral measure, the Girsanov's Theorem, and the Fundamental Theorem of asset pricing as well as a decent exposure to stochastic differential equations.
Teaching methods:
Lectures (2x per week 2 hours) and exercise classes (2x per week 2 hours).

Assessment:
Hand-in exercises 20%, a mid-term 30% and a final exam 50%. For students taking the retake, the final grade is 100% determined by the retake exam.

Retake:
Students with a final grade lower than 4 are eligible to do the retake exam only if they submitted all the hand-in assignments and were present at the final exam.

Language of instructions:
Dutch or English, depending on the participants.

Werkvormen

Hoorcollege

Werkcollege

Toetsing

Eindresultaat

Verplicht | Weging 100% | ECTS 7,5

Ingangseisen en voorkennis

Ingangseisen

Er is geen informatie over verplichte ingangseisen bekend.

Voorkennis

WISB161 Probability theory. An exposure to measure theory and stochastic processes are recommended but not required.

Voertalen

  • Engels

Cursusmomenten

Gerelateerde studies

Tentamens

Er is geen tentamenrooster beschikbaar voor deze cursus

Verplicht materiaal

Er is geen informatie over de verplichte literatuur bekend


Aanbevolen materiaal

  • BOEK
    Stochastic Calculus for Finance II: Continuous time Models. Steven Shreve. Springer-Verlag London Limited 2008. ISBN 978-0-387-40101-0 Dit boek is o.a. te bestellen bij A-Eskwadraat.

Coördinator

prof. dr. ir. C.W. Oosterlee c.w.oosterlee@uu.nl

Docenten

prof. dr. ir. C.W. Oosterlee c.w.oosterlee@uu.nl

Inschrijving

Deze cursus is open voor bijvakkers. Controleer wel of er aanvullende ingangseisen gelden.

Inschrijving
Van maandag 15 september 2025 tot en met vrijdag 26 september 2025

Na-inschrijving
Van maandag 20 oktober 2025 tot en met dinsdag 21 oktober 2025

Inschrijving niet geopend
Permanente link naar de cursuspagina
Laat in de Cursus-Catalogus zien