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

Course content

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.


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 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.

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.


  • 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: 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.

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.
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.
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 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.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 42
  • Class Instruction
  • 30
  • Preparation
  • 86
  • Exam
  • 48
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

August the 2nd to 23th 2021

Go to 'Signup' for
information about registration and enrollment

Information about admission and tuition fee:  Summer schools and for Danes at  Åbent Universitet

and venue for teaching:
Go to 'Remarks'.

For exam and re-sits: Go to 'Exam'.
Department of Economics, Study Council
Contracting department
  • Department of Economics
Contracting faculty
  • Faculty of Social Sciences
Course Coordinators
  • Daniel Brødsgaard   (6-746769393a334368667271316e7831676e)
  • Frederik Emil Amris   (6-7d666a3c3b374368667271316e7831676e)

See "Course Coordinators".

Saved on the 14-06-2021

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