Fixed Income Derivatives: Risk Management and Financial Institutions (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.
MSc programme in Economics – elective course
The course is part of the Financial line at the MSc programme in Economics, symbolized by ‘F’.
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.
Changes to teaching methods due to a pandemic crisis:
The teaching in this course might be changed to either fully or partly online due to a pandemic crisis. If changes are implemented please read the study messages at KUnet or the announcements in the virtual course room on Absalon (for enrolled students).
- 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
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.
3 hours lectures a week from week 36 to 50 (except week 42).
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 (E means Autumn).
You can find the similar information partly in English at
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-E22; [Name of course]”
-Select Report Type: “List – Weekdays”
-Select Period: “Efterår/Autumn”
Press: “ View Timetable”
Please be aware:
- The schedule of the lectures can change without the participants´ acceptance. If this occures, 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.
Individual feedback can be received at the exercise classes.
- 7,5 ECTS
- Type of assessment
Written assignment, 48 hours
- Type of assessment details
- 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 at the written exams.
For further information about allowed aids for the re-examination, please go to the section "Re-exam".
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
for the written exam.
An oral re-examination may be with external assessment.
Criteria for exam assessment
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.
To obtain the grade 12 in this course, 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.
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.
Single subject courses (day)
- Class Instruction
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Go to 'Signup' for information about registration and enrollment.
Information about admission and tuition fee: Master and Exchange Programme, credit students and guest students (Open University)
- For teaching: Go to 'Remarks'.
- For exam and re-sits: Go to 'Exam'.
- Department of Economics, Study Council
- Department of Economics
- Faculty of Social Sciences
- Daniel Brødsgaard (6-776a6c3c3d36466b69757434717b346a71)
- Frederik Emil Amris (6-80696d3f3e3a466b69757434717b346a71)
See "Course Coordinators".
Please read "Remarks" regarding the schedule of the teaching.
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