MAT9770 – Stochastic modelling in energy and commodity markets
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.
PhD candidates from 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 – An Introduction to mathematical finance/MAT2700 – Introduction to mathematical finance and investment theory (continued) 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.
Final oral or written examination. The form of examination will be announced by the teaching staff by 15 October/15 March for the autumn semester and the spring semester respectively.
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.
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.
Grades are awarded on a pass/fail scale. 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.