AØKK08095U Pricing Financial Assets (F)
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 should have acquired the following:
A knowledge of main 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
An understanding of 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
An understanding of the core mathematical methods related to these models including selected proofs and numerical methods
The ability to utilize the methods of arbitrage free pricing to particular pricing and risk hedging problems and to choose the most applicable method
The skill of applying the mathematical toolset to produce quantitative valuations and risk assesments
The ability to understand the limitations of the pricing methods and the risk involved in the practial implementation in both pricing and risk hedging
The ability to 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
The ability to apply arbitrage free pricing methods and risk hedging to new financial instruments, their definition and development
To understand the limitiations of different pricing and hedging methodologies and use this 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.
2 hours lectures 1 to 2 times a week from week 6 to 21 (except holidays).
Timetable and venue:
To see the time and location of lectures please press the link/links under "Se skema" (See schedule) 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-F19; [Name of course]”
-Select Report Type: “List – Weekdays”
-Select Period: “Forår/Spring – Week 5-30”
Press: “ View Timetable”
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"
Registration and information for foreign students not enrolled please find more information at Study Economics.
Læs om uddannelsen og studieordningen på KA uddannelsen i økonomi.
- 7,5 ECTS
- Type of assessment
- Written examination, 3 hours under invigilationThe exam assignment is given in English and must be answered in English.
- Exam registration requirements
- Without aids
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
The course can be selected for external assessment.
- Exam period
The exam takes place at the computers of the university:
12 June 2019
From the middle of the semester the exact time will be available in Digital Exam portal.
Note: In special cases, the exam date can be changed to another day and time within the exam period.
The reexam takes place at the computers of the university:
14 August 2019
During the reexam period the exact time can be seen in Digital Exam.
Note: In special cases, the written reexam can change to another day in the reexam period. Or to an oral exam incl. date, time and place, if only a few students have registered the reexam. This will be informed by the Exam Office.
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