MATS3280 Advanced course in financial mathematics (5 cr)

Study level:
Advanced studies
Grading scale:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024


  • Brownian motion and a short introduction to stochastic integration
  • Arbitrage and completeness
  • The Black-Scholes model
  • Risk neutral pricing and hedging of European options

Learning outcomes

After completing the course, the student knows basics of continuous time stochastic models in finance.

Description of prerequisites

MATS2300 Models in financial mathematics, MATS260 Probability Theory 1 and MATS262 Probability Theory 2

Study materials

  • Study material on the course web page (in Finnish).
  • Alvarez, L., Koskinen, L., Rahoituksen teoriaa ja sovelluksia aktuaareille. Vakuutusvalvontavirasto, 2007.
  • Bingham, N. H., Kiesel, R., Risk-neutral valuation: pricing and hedging of financial derivatives, Springer, 2004.
  • Lamberton, D., Lapeyre, B., Introduction to stochastic calculus applied to finance, 2nd ed., Chapman & Hall, 2008.
  • Lecture notes: Geiss, C., Financial mathematics (Rahoitusteorian stokastisia malleja), 2015.

Completion methods

Method 1

E-learning, educational meetings, final exam.
Evaluation criteria:
The grade is based on the number of points in the final exam. At least half of the points are needed to pass the course.
Select all marked parts
Parts of the completion methods

Participation in teaching (5 cr)

Participation in teaching
Grading scale:
English, Finnish
Study methods:

Verkko-opiskelu, ohjaustapaamiset, lopputentti.