Learning objectives 
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
yield and their relations to forward and futures markets
 Explain and differentiate the contract types in energy markets,
e.g., options on forwards, Asian style derivatives, spread
options
 Explain the special features of energy markets and their
courses and consequences – nonconstant volatility, option smiles,
spikes/jumps and seasonality – in the above mentioned models
 Price derivatives including flow features in the above
mentioned models
 Hedge energy exposures including proxy hedging
techniques

Course prerequisites 
1. 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.
2. Send in a 1 page motivated application, a 1 page CV, and a
graduate grade transcript. Send this to: oecon.eco@cbs.dk no later
than 13 May 2014. Also remember to sign up for the course through
the online registration. 
Prerequisites for registering for the
exam 
Number of mandatory
activities: 1
Compulsory assignments
(assessed approved/not approved)
Oral assignment in groups of no more than 3 students: In the end
of the semester, all students must analyze and orally present a
case analysis done in the last period 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 representation will be
announced in ecampus during the last week of the
course.

Examination 
Oral
exam:

Exam
ECTS 
7,5 
Examination form 
Oral Exam 
Individual or group exam 
Individual 
Duration 
20 min. per student, including examiners'
discussion of grade, and informing plus explaining the
grade 
Preparation time 
No preparation 
Grading scale 
7step scale 
Examiner(s) 
Internal examiner and second internal
examiner 
Exam period 
Winter Term and December/January, Provisional:
The exam is held in December. The retake is held in
January. 
Aids allowed to bring
to the exam 
Closed Book 
Makeup exam/reexam 
Same examination form as the ordinary exam

Description of the exam
procedure
Oral examination, 20 minutes, no preparation time. Prepared
slide show is a part of the examination. The examination has two
parts 1) (10 minutes) Three weeks before the exam, 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 other exam aids
for the exam. At the start of the examination, the student chooses
one of the topics at random and immediately thereafter gives the
presentation. 2) (8 minutes) The student is asked questions in
parts of the curriculum different from the topic covered in the
part.
Slides are 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.
The concepts learnt in Derivatives and Risk Management
are extended to model commodity markets. The course is
devoted to understanding commodity markets and corresponding
derivatives markets. We emphasize the concept of convenience yields
and its relations to forwards and futures markets of commodities.
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, nonconstant volatility
and the physical character of the products creates many different
markets with lower liquidity comparing to other financial
markets.

Teaching methods 
 Class lectures
 Case study
 Exercises 
Further Information 
Changes in course schedule may occur
Tuesday 08.0009.40, week 3641
Thursday 08.0009.40, week 3641, 4348 
Expected literature 
 Barlow: `'A Diffusion Model for Electricity Prices,"
Mathematical Finance, Vol. 12, No. 4, 2002, pp. 287298.
 Bendt, Bendt, and Koekebakker: Stochastic Modeling of
Electricity and Related Markets, World Scientific Publishing
Company, 2008, pp. 117.
 Bertus, Godbey and Hilliard: \Minimum Variance Cross Hedging
Under MeanReverting 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. 4183.
 Erb, Luthi, and Otziger: Schwartz (1997) TwoFactor Model:
technical note,", 2010.
 Geman: Commodities and Commodity Derivatives, Wiley, 2005, pp.
201217 and 236249.
 Gibson and Schwartz: \Stochastic convenience Yield and the
Pricing of Oil Contingent Claims", The Journal of Finance,
Vol. 45, No. 3, 1990, pp. 959976.
 Lucia and Schwartz: Electricity Prices and Power Derivatives :
Evidence from the Nordic Power Exchange," Review of
Derivatives Research, Vol. 5, 2002, pp. 550.
 Miltersen: Commodity price modelling that matches current
observables: a new approach, "Quantitative Finance, Vol. 3,
No. 1, 2003, pp. 5158.
 Miltersen and Schwartz: Pricing of Options on Commodity Futures
with Stochastic Term Structures of Convenience Yields and Interest
Rates," Journal of Financial and Quantitative Analysis, Vol.
33, No. 1, 1998, pp. 3359.
 Oum and Oren: Hedging Quantity Risks with Standard Power
Options in a Competitive Wholesale Electricity Market", Naval
Research Logistics, Vol. 53, 2006, pp. 697712.
 Schwartz: \The Stochastic Behavior of Commodity Prices:
Implications for Valuation and Hedging," The Journal of
Finance, Vol. 52, No. 3, 1997, pp. 923973.
 Schwartz and Smith: \Shortterm variations and longterm
dynamics in commodity prices, "Management Science, Vol. 46,
No. 7, pp. 893911.
 Sørensen: Modeling Seasonality in Agricultural Commodity
Futures," Journal of Futures Markets, Vol. 22, No. 5, 2002,
pp. 393{426.
 The case material
 Teaching notes, presentations and exercises
 Mathematical Methods and Models in Finance. Lecture
notes.
