MAT4770 – Stochastic Modelling in Energy and Commodity Markets
Course description
Schedule, syllabus and examination date
Course content
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 course 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.
Learning outcome
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.
Admission to the course
Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.
Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.
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)
Overlapping courses
- 10 credits overlap with MAT9770 – Stokastisk modellering i energi og råvaremarkeder.
Teaching
4 hours of lectures/exercises per week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Examination
Final written exam or final oral exam, which counts 100 % towards the final grade.
The form of examination will be announced by the lecturer by 1 October/1 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.
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: MAT9770 – Stokastisk modellering i energi og råvaremarkeder
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.
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.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.