MAT9770 – Stochastic Modelling in Energy and Commodity Markets
Schedule, syllabus and examination date
Exams after the reopening
As a general rule, exams will be conducted without physical attendance in the autumn of 2021, even after the reopening. See the semester page for information about the form of examination in your course. See also more information about examination at the MN Faculty in 2021.
The course gives an introduction to dynamic stochastic models for prices in commodity and energy markets. Classical factor models based on Ornstein-Uhlenbeck processes are analyzed, and extended to so-called continuous-time autoregressive processes with a moving average. The stochastic processes are driven by Brownian motion and simple jump processes to model sudden price changes (spikes), which are characteristic for some energy markets (for example, power). In the course we also look at dynamic modelling of temperature, wind and sun, and analyze these in the context of energy markets, but also the independent markets for weather products. Particular case here is the seasonal variations. Further pricing techniques for forward contracts on commodity and energy are developed, in addition to relevant derivatives as "spread" and quanto options. The theory on pricing measures and risk premium is presented, and the term structure of volatility analyzed (the so-called Samuelson effect).
The topic will focus on making the models and analysis operational in practical applications. Techniques for estimation and calibration are presented, in addition to methods for numerical simulation.
After completing the course you will:
- know and understand the classical stochastic models for commodity and energy markets
- know how to establish forward prices based on factor models in the spot market
- know how to estimate and simulate the models, and apply these in different markets, like the market for weather derivatives
- understand important notions as pricing measure, market price of risk and the risk premium
- know how to analyze and price important derivatives in commodity and energy markets
- be able to present, on a scientific level, a short thesis on a chosen topic of relevance, selected in collaboration with the lecturer.
Admission to the course
PhD candidates from the Faculty of Mathematics and Natural Sciences at the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Recommended previous knowledge
- STK-MAT3700 – Introduction to Mathematical Finance and Investment Theory or STK4510 – Introduction to methods and techniques in financial mathematics (discontinued)
- MAT4720 – Stochastic Analysis and Stochastic Differential Equations or MAT4701 – Stochastic analysis with applications (continued)
- 10 credits overlap with MAT4770 – Stochastic Modelling in Energy and Commodity Markets.
4 hours of lectures/exercises every week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Final written exam 4 hours or final oral exam, which counts 100 % towards the final grade.
The form of examination will be announced by the lecturer by 15 October/15 March for the autumn semester and the spring semester respectively.
This course has 1 mandatory assignment that must be approved before you can sit the final exam.
In addition, each PhD candidate is expected to give a one hour oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT4770 – Stochastic Modelling in Energy and Commodity Markets
Examination support material
No examination support material is allowed.
Language of examination
Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more: