STK-MAT4700 – An Introduction to mathematical finance

Schedule, syllabus and examination date

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Course content

The course will give an introduction to the most important notions and problems in mathematical finance. The theory of arbitrage for pricing and hedging derivatives (options) will be studied in the context of discrete and continuous time stochastic models, with the famous Black and Scholes option pricing formula as a highlight. Moreover the course will focus on the theory of investments with special stress given to utility optimization and the Markowitz' theory for optimal portfolio choice. 

Learning outcome

The students will understand the underlying principles of modern finance and investments theory. They will be given the mathematical theoretical and practical skills to be used in quantifying the price of financial contracts, in computing the hedging strategies and in making investments choices which balance profit and risk. More particularly:

  • develop hedging strategies for derivatives in tree-models;
  • price using no-arbitrage and hedging principles in tree-models;
  • know the concept of risk-neutral probability;
  • develop the Black-Scholes option pricing formula as a limit of tree-model;
  • apply the Black-Scholes formula to price and hedge plain-vanilla options in finance;
  • can create portfolios that balance profit and risk optimally;
  • master LaTeX as an electronic tool for writing mathematics.


Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.

Overlapping courses

*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 


4 hours of lectures/exercises per week throughout the semester.


1 mandatory assignment written with (LaTeX), the typesetting software for academic writing in mathematics.

The final written exam counts 100% for the grade.



Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Explanations and appeals

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.


The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course






Every autumn


Every autumn

Teaching language


The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.