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2016/2017  KAN-COECV3004U  Energy Finance: Quantitative Modeling and Real Options

English Title
Energy Finance: Quantitative Modeling and Real Options

Course information

Language English
Course ECTS 7.5 ECTS
Type Elective
Level Full Degree Master
Duration One Semester
Start time of the course Autumn
Timetable Course schedule will be posted at calendar.cbs.dk
Study board
Study Board for MSc in Advanced Economics and Finance
Course coordinator
  • Kristian Miltersen - Department of Finance (FI)
Contact information: https:/​/​e-campus.dk/​studium/​kontakt
Main academic disciplines
  • Finance
  • Statistics and quantitative methods
Last updated on 04-03-2016
Learning objectives
To achieve the grade 12, students should meet the following learning objectives with no or only minor mistakes or errors: Upon the end of the course the students will be able to:
  • Model asset prices in continuous time using stochastic processes
  • Model commodity markets including the concept of convenience yields and their relations to forwards and futures markets
  • Explain the special features of energy markets and their courses and consequences – non-constant volatility, spikes/jumps and seasonality – in the above mentioned models
  • Price derivatives and hedge exposures in the above mentioned models
  • Apply real options analysis to continuous time models
  • Identify real options and apply its analysis to managerial decision making
Course prerequisites
Please note that this course is taught at an elite level and requires a high level of mathematics and probability theory. More specifically, it requires Derivatives and Risk Management from the MSc in Advanced Economics and Finance (cand.oecon) program or similar curriculum. Knowledge of econometrics is an advantage.
Prerequisites for registering for the exam
Number of mandatory activities: 1
Compulsory assignments (assessed approved/not approved)
Oral assignment in groups: In the last part of the course, all students must analyze and orally present their results of a case study. The presentations will take place during the last class of the course. The group size will be announced during the first weeks of the course.

In case the oral assignment is not approved, the student will be given the possibility to make a new oral presentation before the ordinary exam. The exact date of this re-presentation will be announced on MyCBS during the last week of the course.
Energy Finance: Quantitative Modeling and Real Options:
Exam ECTS 7,5
Examination form Oral Exam
Individual or group exam Individual exam
Duration 20 min. per student, including examiners' discussion of grade, and informing plus explaining the grade
Preparation time No preparation
Grading scale 7-step scale
Examiner(s) Internal examiner and second internal examiner
Exam period Winter
Aids allowed to bring to the exam Closed book
Make-up exam/re-exam
Same examination form as the ordinary exam
Description of the exam procedure

Oral examination, 20 minutes, no preparation time. Presentation file prepared in advance is a part of the examination. The examination has two parts.  Part One (10 minutes): During the last class of the semester, the students are given a number of topics for which they have to prepare a 10 minutes presentation. They should use slides (brought to the exam on a USB stick), but they are not allowed to bring any other exam aids for the exam. At the start of the examination, the student draws one of the topics at random and immediately thereafter gives the presentation. Part Two (8 minutes): The student is asked questions in parts of the curriculum different from the topic covered in Part One.

Presentation File is allowed for the first part of the examination.

Course content and structure

The course provides the students with a profound knowledge of key concepts, relations, and models in commodity markets in general and energy markets in particular. Further, the course provides the students with knowledge of real options analysis and how this can be applied to managerial decision making.
The concepts learnt in Derivatives and Risk Management are extended to model commodity markets. The course is devoted to understanding commodity markets, corresponding derivatives markets, and real options.


The course focuses on energy markets in particular. Energy markets are challenging due to the number of cross product substitutions, the various competitive settings in the sector, the institutional details of the distribution channels of the different products, the different market structures, and the highly sophisticated derivatives markets. In particular, energy prices experience seasonality, mean reversion, spikes/jumps, and non-constant volatility.   Moreover, the physical character of the products creates many differentiated markets with lower liquidity comparing to other financial markets.  Therefore investment decisions related to these markets are also challenging and here real options analysis turns out to be very suitable and applicable.

Teaching methods
- Class lectures
- Case study
- Exercises
Student workload
Lectures 30 hours
Exercises 6 hours
Preparation for case, lectures, exercises, and exam 170 hours
Expected literature
  • Barlow: `'A Diffusion Model for Electricity Prices," Mathematical Finance, Vol. 12, No. 4, 2002, pp. 287-298.
  • Bendt, Bendt, and Koekebakker: Stochastic Modeling of Electricity and Related Markets, World Scientific Publishing Company, 2008, pp. 1-17.
  • Bertus, Godbey and Hilliard: "Minimum Variance Cross Hedging Under Mean-Reverting Spreads, Stochastic Convenience Yields, and Jumps: Application to the Airline Industry", The Journal of Futures Markets, 2009.
  • Carmona and Coulon: "A survey of commodity markets and structural models for electricity prices," Quantitative Energy Finance, 2014, pp. 41-83.
  • Dixit and Pindyck:. "Investment under uncertainty". Princeton University Press, 1994.
  • Erb, Luthi, and Otziger: "Schwartz (1997) Two-Factor Model: technical note,", 2010.
  • Geman: "Commodities and Commodity Derivatives", Wiley, 2005, pp. 201-217 and 236-249.
  • Gibson and Schwartz: "Stochastic convenience Yield and the Pricing of Oil Contingent Claims", The Journal of Finance, Vol. 45, No. 3, 1990, pp. 959-976.
  • Lucia and Schwartz: "Electricity Prices and Power Derivatives : Evidence from the Nordic Power Exchange", Review of Derivatives Research, Vol. 5, 2002, pp. 5-50.
  • Oum and Oren: "Hedging Quantity Risks with Standard Power Options in a Competitive Wholesale Electricity Market", Naval Research Logistics, Vol. 53, 2006, pp. 697-712.
  • Schwartz: "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging", The Journal of Finance, Vol. 52, No. 3, 1997, pp. 923-973.
  • Schwartz and Smith: "Short-term variations and long-term dynamics in commodity prices", Management Science, Vol. 46, No. 7, pp. 893-911.
  • The case material
  • Teaching notes, presentations, and exercises
  • Mathematical Methods and Models in Finance. Lecture notes.
Last updated on 04-03-2016