AØKA08204U Fixed Income Derivatives: Risk Management and Financial Institutions

Volume 2013/2014
MSc in Economics
Over the last decades there has been an explosive growth in the use of fixed income derivatives. Following this growth derivatives are now commonly used not only in financial institutions but in many private and public entities. At the same time, the widespread use of derivatives is often blamed for playing a role in escalating and prolonging the current financial crisis. Obtaining a thorough understanding of the pricing and risk management of derivatives is therefore more relevant than ever before.

Using the quantitative tools employed in industry, students will learn how to characterize financial risks and how to employ derivatives to mitigate these. As such the course is relevant for students interested in pursuing careers in investment banking, in a public or private treasury operation or within the regulating authorities.
Learning Outcome

The course will give a thorough understanding of fixed income derivatives, with a focus on how they are used in practice. Fixed income markets, including interest rate swaps, swaptions, caps, floors and credit default swaps, are some of the most actively traded financial markets, and underpin much of the banking system.

The lectures will be quite quantitative in nature, as the main pricing models will be derived and explained in detail. Nonetheless, they will also cover various market standards to ensure that the models are practically applicable. The focus will be on products that are actually traded - how they work, how they are priced and how the risk inherent in them is assessed and hedged - in a framework that is as close to reality as possible.

Next to the lectures, students will spend considerable time building pricing and risk management models using Excel and VBA. By the end of the course, students will have built a small pricing library that is as close to market standards as possible.

Upon completing the course, the excellent student will:

  • Understand the mechanics underlying a range of fixed income derivatives
  • Know the main terminology used in the industry
  • Appreciate the motivations of various market participants behind the use of fixed income derivatives
  • Understand and be able to apply the models used to price the most common instruments
  • Be able to assess and quantify the risks associated with these instruments, and how these risks can be hedged
  • Have implemented pricing and risk analysis models in Excel and VBA resembling those used in practice

As the course is oriented towards the use of derivatives in practice, students are required to demonstrate a thorough understanding of all aspects surrounding derivatives – from the basic legal framework to the practical implementation of pricing models using Excel and VBA – to obtain the grade 12.

The syllabus for the course is as follows:
• Linderstrøm (2010)
• Hagan & West (2006), pages 89-100
• Hagan, Kumar, Lesniewski & Woodward (2002) (excl. the appendices)
• Hagan (2003)
• The lecture slides


Hagan, P. S. (2003), ‘Convexity conumdrums: Pricing cms swaps, caps, and floors’, Wilmott
Magazine pp. 38–44,.
Hagan, P. S., Kumar, D., Lesniewski, A. S. & Woodward, D. E. (2002), ‘Managing smile risk’,
Wilmott Magazine pp. 84–108.
Hagan, P. S. & West, G. (2006), ‘Interpolation methods for curve construction’, Applied Mathematical
Finance 13(2), 89–129.
Linderstrøm, M. D. (2010), Fixed income derivatives. Lecture Notes, University of Copenhagen.
The course is not intended to be an introductory course. Students are thus assumed to have some prior knowledge of derivatives and financial markets from e.g. “Corporate Finance and Incentives” or “Finansieringsteori / Asset Pricing”.
It is important to stress that an integral part of this course will be programming in VBA. While no prior knowledge of VBA is assumed, students are expected to have some basic programming experience e.g. SAS.
In exchange for a reading list that in terms of pages will be short, students are expected to devote considerable time over the course of the semester to implement pricing functions in VBA/Excel. To facilitate this, lectures will address not only the relevant theory but also include computer sessions that address practical issues.
3 hours of lectures per week for 14 weeks.

Lectures supplemented with computer sessions.
  • Category
  • Hours
  • Exam
  • 48
  • Lectures
  • 42
  • Preparation
  • 116
  • Total
  • 206
7,5 ECTS
Type of assessment
Written assignment, 48 hours
An individual 48 hours take-home assignment.
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
100 % censurship
Exam period
Will be updated before the start of the semester
Same as ordinary. But if only a few students have registered for the re-exam, the exam might change to an oral exams with a synopsis to be handed in. This means that the examination date also will change.
Criteria for exam assesment
The Student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.