Pricing Financial Assets (F)

Course 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.

Education

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

Learning outcome

After completing the course, the student should have acquired the following:

Knowledge:

  • 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

Skills:

  • 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

Competences:

  • 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

 

Main textbook:

John C. Hull: "Options, Futures and Other Derivatives," 8th edition 2012, Pearson Education, Prentice-Hall. ISBN 978-0-13-216494-8.
Notes:

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

Syllabus:
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.

The course requires certain knowledge of basic microeconomics and elementary mathematics and statistics. The course also requires the BA-course in finance, including a 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).

Schedule:
2 hours lectures 1 to 2 times a week from week 6 to 20 (except holidays).


Timetable and venue:
The schedule for the semester spring 2018 will be available no later than 7th of November 2017

ECTS
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
at the computers at the university. The exam assignment is given in English and must be answered in English.
Aid
Without aids
Marking scale
7-point grading scale
Censorship form
External censorship
if chosen by the Head of Studies.
Criteria for exam assessment

Students are assessed on the extent to which they master the learning outcome for the course.

To receive the top grade, the student must be able to demonstrate in an excellent manner that he or she has acquired 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):

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

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 42
  • Preparation
  • 161
  • Exam
  • 3
  • English
  • 206