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," 8th edition 2012, Pearson Education, Prentice-Hall. ISBN 978-0-13-216494-8.
- Frank Hansen: "Supplements in Finance Theory,” 2009, University of Copenhagen. Can be downloaded from the course website.
- The binomial model; Hull Chapter 12.
- 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 13.
- The Black-Scholes-Merton model; Hull Chapter 14.
- Options on stock indices and currencies; Hull Chapter 16.
- Futures options; Hull Chapter 17.
- The Greek letters; Hull Chapter 18.
- Credit risk; Hull Chapter 23.
- Credit derivatives; Hull Chapter 24.
- Martingales and measures; Hull Chapter 27.
- Interest Rate Derivatives: The standard market models; Hull Chapter 28.
- Interest Rate Derivatives: Models of the short rate; Hull Chapter 30.
- Interest Rate Derivatives: HJM and LMM; Hull Chapter 31.
It is strongly recommended that the course "Corporate Finance and Incentives" 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.
In case of a pandemic like Corona the teaching in this course may be changed to be taught either fully or partly online. For further information, see the course room on Absalon.
2 hours lectures 1 to 2 times a week from week 6 to 21 (except holidays).
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-F21; [Name of course]”
-Select Report Type: “List – Weekdays”
-Select Period: “Forår/Spring – Week 5-30”
Press: “ View Timetable”
For gæste- og enkelfagsstuderende: Tilmelding via Uddannelse i Økonomi.
- 7,5 ECTS
- Type of assessment
- Written examination, 3 hours under invigilationin the exam venues of the university.
The exam assignment is given in English and must be answered in English.
In the event that this summer's exams have to be conducted as online exams due to COVID-19, the exam form will be a 3 H take-home exam with aids. The reexam will be the same as the rescheduled ordinary exam, but possibly online orally if only few students register.
- Exam registration requirements
There are no requirements during the course that the student has to fulfill to be able to sit the exam.
- Without aids
for the written exam.
In case of an oral reexam, please go to the section "Reexam" for further information about allowed aids.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
for the written exam. The exam may be chosen for external censorship by random check.
- Exam period
The regular exam takes place:
24 June 2021
The exact time and room will be available in the Digital Exam from the middle of the semester.
In special cases, the exam date can be changed to another time and day. In case of COVID-19 restrictions, please refer to the "Type of assessment" section.
The written reexam takes place:
19 August 2021
NOTE: If only few students register for the written re-exam, the re-exam might change to a 20 minutes oral examination without preparation time.
No aids allowed during the examination.
If changed to an oral re-exam, the exam date, time and place might change as well. The Examination's Office then informs the students by KU e-mail. In case of COVID-19 restrictions, please refer to the "Type of assessment" section.
Info is available in Digital Exam early August.
Criteria for exam assesment
Students are assessed on the extent to which they master the learning outcome for the course.
To receive the top grade, 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.
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