AØKK08095U Pricing Financial Assets (F)
MSc programme in Economics – elective course
The course is part of the Financial line at the MSc programme in Economics, symbolized by ‘F’.
The course covers valuation of financial assets and derivatives with an emphasis on arbitrage pricing and hedging. Different methods for arbitrage free pricing are introduced with the purpose of providing the student with a toolset that can be utilized most suitably for the valuation problem at hand. The theory and methods are applied to core financial derivatives which are introduced and given a rigorous definition with a further coverage of the institutional settings and conventions that has developed for such contracts and the trading thereof. Derivatives are covered in abstract generality as well as in practical implementations in the form of equity, commodity, currency, credit and interest rate derivatives.
After completing the course the student is expected to be able to:
Define the main types of financial assets and derivatives, their definitions and their risk characteristics as well as the institutional framework for such contracts and the trading thereof.
Account for the concept of arbitrage free pricing, the importance of this approach in modern financial theory, and the various methods that can be applied for such pricing.
Reflect on the core mathematical methods related to these models including selected proofs and numerical methods.
Utilize the methods of arbitrage free pricing to particular pricing and risk hedging problems and to choose the most applicable method.
Apply the mathematical toolset to produce quantitative valuations and risk assesments.
Evaluate the limitations of the pricing methods and the risk involved in the practial implementation in both pricing and risk hedging.
Extract from a complicated practical setting the relevant financial risk elements that can be analyzed and to adapt the methodology to the problem at hand.
Apply arbitrage free pricing methods and risk hedging to new financial instruments, their definition and development.
Master the limitiations of different pricing and hedging methodologies to modify the approach and/or make sound judgements on the direction and size of pricing errors and residual, non-hedged risks.
- John C. Hull: "Options, Futures and Other Derivatives," 10th edition 2018, Pearson Education, Prentice-Hall. ISBN 978-0-13-463149-3 (or later edition).
- Frank Hansen: "Supplements in Finance Theory,” 2009, University of Copenhagen. Can be downloaded from the course website.
- The binomial model; Hull Chapter 13.
- The one-period model; Suppl. Section 1, pp. 2-5.
- The multi-period model; Suppl. Section 2, pp. 7-14.
- Wiener processes and Ito's lemma; Hull Chapter 14.
- The Black-Scholes-Merton model; Hull Chapter 15.
- Options on stock indices and currencies; Hull Chapter 17.
- Futures options; Hull Chapter 18.
- The Greek letters; Hull Chapter 19.
- Credit risk; Hull Chapter 24.
- Credit derivatives; Hull Chapter 25.
- Martingales and measures; Hull Chapter 26.
- Interest Rate Derivatives: The standard market models; Hull Chapter 29.
- Interest Rate Derivatives: Models of the short rate; Hull Chapter 31-32.
- Interest Rate Derivatives: HJM and LMM; Hull Chapter 33.
It is strongly recommended that a similar course as "Corporate Finance and Incentives" at the Bachelor programme in Economics, University of Copenhagen, have been followed. Including having knowledge of financial derivatives as forwards, futures and call and put options as they are covered in the first chapters of the main textbook that are not included in the syllabus.
Restrictions due to pandemic crisis:
The teaching in this course may be changed to be taught either fully or partly online due to a pandemic crisis like COVID-19. In case of changes and further information, please read the study messages in KUnet or the announcements in the course room on Absalon (for enrolled students).
2 hours lectures 1 to 2 times a week from week 6 to 20.
The overall schema for the Master can be seen at KUnet:
MSc in Economics => "courses and teaching" => "Planning and overview" => "Your timetable"
KA i Økonomi => "Kurser og undervisning" => "Planlægning og overblik" => "Dit skema"
Timetable and venue:
To see the time and location of lectures please press the link under "Timetable"/"Se skema" at the right side of this page (F means Spring).
You can find the similar information partly in English at
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-F22; [Name of course]”
-Select Report Type: “List – Weekdays”
-Select Period: “Forår/Spring – Week 5-30”
Press: “ View Timetable”
Please be aware:
- The schedule of the lectures can be changed without the participants´ acceptance. If this happens you can see the new schedule in your personal timetable at KUnet, in the app myUCPH and through the links in the right side and the link above.
- It is the students´s own responsibility continuously throughout the study to stay informed about their study, their teaching, their schedule, their exams etc. through the curriculum of the study programme, the study pages at KUnet, student messages, the course description, the Digital Exam portal, Absalon, the personal schema at KUnet and myUCPH app etc.
Foreign students and guests: Information about admission requirements, application, tuition fee, registration at Study Economics.
Please read the curriculum before enrolment.
Gæste- og enkelfagsstuderende: Tilmelding via Uddannelse i Økonomi.
- 7,5 ECTS
- Type of assessment
- Written examination, 3 hours under invigilationas an ITX-exam in the exam venues of the university.
The exam assignment is given in English and must be answered in English.
Changes due to Coronavirus:
In the event that COVID-19 restrictions may affect the conduction of the ITX-exams, the written exam and the re-sit exam will be changed to a 3 hours take-home exam with all aids. If done so, the changes will be announced in study messages at KUnet and in the Digital Exam portal.
The take-home exam is an individual exam and it is not allowed to communicate with any one about the exam assignment nor the solution at all. It is also prohibited to distribute data and other information at all. If this or alike actions happens, it will be regarded as cheating and plagiarism.
- Exam registration requirements
There are no requirements during the course that the student has to fulfill to be able to sit the exam.
No aids allowed at the written ITX-exam.
If the ITX-exam is changed to a take-home exam due to COVID-19, the written take-home exam will be with all aids.
Information about allowed aids for the re-examination, please go to the section "Re-exam".
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
at the written exam.
The written ITX-exam may be chosen for external assessment by random sample.
An oral re-examination may be with external assessment.
- Exam period
The regular exam takes place:
23 June 2022
The exact time and place will be available in Digital Exam from the middle of the semester.
The Department can change the exam to another type, day, time and place than announced.
The written reexam takes place:
18 August 2022
If few students register, it might change to a 20 minutes oral examination without preparation time.
No aids allowed during the examination.
Due to COVID-19, the re-sit might change to 20 minutes oral ONLINE exam with all aids, without preparation time.
Exact type, day, time and place is available in Digital Exam in August.
The Department can change to another type, day, time and place than announced.
Criteria for exam assesment
Students are assessed on the extent to which they master the learning outcome for the course.
In order to obtain the top grade “12”, the student must with no or only a few minor weaknesses be able to demonstrate an excellent performance displaying a high level of command of all aspects of the relevant material and can make use of the knowledge, skills and competencies listed in the learning outcomes.
In this course the exam assessment is subject to the following criteria for an excellent performance (a grade of 12):
The ability to define the types of financial assets and derivatives, of their definitions and of their risk characteristics as well as the institutional framework for such contracts and the trading thereof as covered by the syllabus
The ability to explain the concept of arbitrage free pricing and the various methods that can be applied for such pricing as covered by the syllabus
The ability to explain mathematical and numerical methods related to these models and to reproduce simple proofs
The ability to use methods of arbitrage free pricing, including both discrete and continuous time models, to select simple pricing and risk hedging problems
The ability to explain the limitations of the pricing methods and give perspectives on risk involved in the practical implementation in a given problem
The ability to demonstrate the understanding of the financial risk element embedded in a given theoretical or practical problem
The ability to apply arbitrage free pricing methods and risk hedging to such a problem, including to a financial instrument that is a variations on, but not directly included among, instruments covered by the syllabus
The ability to comment on the direction and size of pricing errors and residual, non-hedged risks
In order to obtain the passing grade “02”, the student must in a satisfactory way be able to demonstrate a minimal acceptable level of the knowledge, skills and competencies listed in the learning outcomes.
- Course code
- 7,5 ECTS
- Full Degree Master
- 1 semester
- Go to 'Signup' for
information about registration and enrollment.
- and venue:
- For teaching: Go to 'Remarks'.
- For exam and re-sits: Go to 'Exam'.
- Course is also available as continuing and professional education
- Study board
- Department of Economics, Study Council
- Department of Economics
- Faculty of Social Sciences
- Henrik Olejasz Larsen (21-6c6972766d6f327370696e65777e327065767769724469677372326f7932686f)
See ‘Course Coordinators’
Please read "Remarks" regarding the schedule of the teaching.