AØKA08204U Summer school 2021: Fixed Income Derivatives: Risk Management and Financial Institutions (F)

Volume 2021/2022

MSc programme in Economics – elective course


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


Over the last decades there has been an explosive growth in the use of fixed income derivatives. Derivatives are now commonly used not only in financial institutions but also in many private and public entities. At the same time, the widespread use of derivatives is often blamed for playing a destabilizing role in the recent financial crisis. Obtaining a thorough understanding of the pricing, trading 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 derivatives can be used 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 regulatory authorities.


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


In addition to the financial products traded we will give an up to date overview of the current regulatory stance regarding clearing and margin requirements and how this is related to pricing. Specifically how this relates to counterparty specific value adjustments to the market price of derivatives.


The lectures will be quite quantitative in nature, as the main pricing models will be derived and explained in detail. Nonetheless, lectures will also focus on how derivatives are traded in practice and considerable time will be spent on covering various market standards to ensure that the models are practically applicable. The focus will be on products that are actually traded in a framework that is as close to reality as possible.


By the end of the course, students will have built a small pricing library that is as close to market standards as possible.

Learning Outcome

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



  • Identify the mechanics underlying a range of fixed income derivatives.
  • Account for how derivatives are traded and priced in the market place.
  • Identify and account for the risk is quantified and how they are hedged.
  • Reflect on the motivations of various market participants behind the use of fixed income derivatives.



  • Use pricing models in Excel/VBA to compute prices and hedge ratios of plain vanilla derivatives
  • Assess and quantify the risks associated with different instruments and construct an appropriate hedge
  • Assess the appropriateness of different pricing models in a given situation
  • Critically assess news media coverage of derivatives
  • Apply models and concepts in a real-world setting, e.g. by devising and executing an interest rate hedge for a corporate bond issue
  • Identify badly structured derivatives that could lead to disastrous outcomes for both counterparties
  • Independently implement standard (closed-form) pricing models in Excel/VBA 




  • Plan and implement pricing and risk analysis models in Excel and VBA in new solutions. 
  • Master and implement relevant financial models and concepts in new and complex contexts.


  • Linderstrøm's Fixed Income Derivatives Lecture Notes (approx. 90 pages)
  • The lecture slides + notes
  • Hagan, Kumar, Lesniewski & Woodward (2002) (excl. the appendices)
  • Hagan (2003)
  • Hagan & West (2006), pp. 89-100
  • News articles



  • 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), pp. 89–129
  • Linderstrøm, M. D. (2010), Fixed income derivatives. Lecture Notes, University of Copenhagen
  • Notes provided by the lecturers.


The course is not intended to be an introductory course. Students are assumed to have prior knowledge of fixed income markets and basic Black-Scholes theory (e.g. from “Corporate Finance and Incentives” or “Pricing Financial Assets ”), at least at the level of the Hull textbook ("Options, futures, and other derivatives").

Furthermore, 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 and some familiarity with Excel is a definite plus.
Lectures, exercise classes and assignments.

The teaching (lectures and exercise classes) is conducted physically on campus.
The teaching can also be followed online. Check out Absalon how to access the virtuel teaching.
Lectures: 9.00-12.00 (no teaching in the weekends)
Exercise classes: 12.00-14.00

Timetable and venue:
Press the link:
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-B5-5F21; [Name of course]””
-Select Report Type: "List - Week Days"
-Select Period: “Efterår/Autumn – Week 31-4”
Press: “ View Timetable”

Please note that it is the student´s own responsibility to constantly be aware of and search for information about the study, teaching, schedule, exam etc. through the study pages, the course description, the digital exam portal, Absalon, KUnet, myUCPH app, curriculum etc.
  • Category
  • Hours
  • Lectures
  • 42
  • Class Instruction
  • 30
  • Preparation
  • 86
  • Exam
  • 48
  • Total
  • 206
Continuous feedback during the course of the semester


Individual feedback can be received at the exercise classes.

7,5 ECTS
Type of assessment
Written assignment, 48 hours
individual take-home exam. It is not allowed to collaborate on the assignment with anyone.
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.


All aids allowed

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 written exam takes place

from August 21th at 10 to August 23 at 10 AM, 2021


Note: In special cases, the exam date can be changed to another day.


Exam information:

More information about examination, rules etc.: Master students (UK) and  Master students (DK)



The written reexam will take place

in the period December 2021 - January 2022


NOTE: If only few students register for the written re-exam, the re-exam might change to a 20 minutes oral examination with 20 minutes preparation time.

All written aids allowed during the preparation time, no aids allowed during the examination.

In case of Covid-19, the oral reexam may be changed to an 20 min. online oral re-exam with all aids, but without preparation time.

The Examination's Office then informs the students by KU e-mail.


Reexam info:

Info is available in Digital Exam early December.

More info at 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.


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.


To obtain the grade 12, students are required to demonstrate a thorough understanding of all aspects surrounding fixed income and credit derivatives – from the basic legal framework to the practical implementation of pricing models using Excel and VBA.