AØKK08095U Pricing Financial Assets (F)

Volume 2023/2024
Education

MSc programme in Economics – elective course


The course is part of the Financial line at the MSc programme in Economics,   symbolized by ‘F’.

Content

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.

Learning Outcome

After completing the course the student is expected to be able to:

 

Knowledge:

  • 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.

Skills:

  • 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.

Competences:

  • 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.

 

Main textbook:

  • John C. Hull: "Options, Futures and Other Derivatives," 10th edition 2018, Pearson Education, Prentice-Hall. ISBN 978-0-13-463149-3 (or later edition).

 

Notes:

  • Frank Hansen: "Supplements in Finance Theory,” 2009, University of Copenhagen. Can be downloaded from the course website.

 

Syllabus:

  • 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.
The course requires certain knowledge of basic microeconomics and elementary mathematics and statistics.

It is strongly recommended that a similar course as "Corporate Finance and Incentives" or "Financial Decision Making" at the study 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.
Lectures.
Schedule:
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).


Please be aware:
- The schedule of the lectures can change without the participants´ acceptance. If this occure, you can see the new schedule in your personal timetable at KUnet, in the app myUCPH and through the links in the right side of this course description 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.
  • Category
  • Hours
  • Lectures
  • 42
  • Preparation
  • 161
  • Exam
  • 3
  • Total
  • 206
Oral
Collective
Credit
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
Type of assessment details
ITX-exam in the exam venues of the university.
The exam assignment is given in English and must be answered in English.
Exam registration requirements

There are no requirements during the course that the student has to fulfill to be able to sit the exam.

Aid

No aids allowed at the written ITX-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.
Exam period

Exam information:

The exact time and place will be available in Digital Exam from the middle of the semester. In special cases decided by the Department, the exam can change to another place, type, day and/or time than announced. 

More information about examination, rules, aids etc. at Master (UK) and Master (DK).

Re-exam

Same as the ordinary exam. 

Exam information:

Exact type, day, time and place: See Digital Exam in February/August. In special cases decided by the Department, the exam can change to another place, type, day and/or time than announced.

More info: Master(UK) and Master(DK). 

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):

Knowledge

  • 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

Skills

  • 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

Competences

  • 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.