Financial Econometrics A (F)

Course content

The course gives an introduction to the econometric analysis of asset returns, with emphasis on econometric modeling of time-varying volatility. Various applications are considered, including risk management and derivatives pricing.


We consider three different econometric approaches to time-varying volatility: (1) GARCH models, (2) Stochastic Volatility models (SV), and (3) Realized Volatility (RV).


The stochastic properties of the processes are analyzed in detail, using new statistical theory such as applying the so-called drift criterion. Estimation of time-varying volatility will primarily be likelihood-based, including non-linear optimization and filtering methods. Econometric analysis is given of the estimators, and sufficient conditions for asymptotic normality are derived.


All modeling is illustrated empirically using standard software packages as OxMetrics 8.0. In addition, an introduction is given to simple programming as needed for implementation of e.g. risk-measures.


MSc programme in Economics – elective course

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


Bacheloruddannelsen i økonomi – valgfag på 3. år

The Danish BSc programme in Economics - elective at the 3rd year


The course is open to:

  • Exchange and Guest students from abroad
  • Credit students from Danish Universities
  • Open University students
Learning outcome

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



  • Account for properties of stochastic processes used for volatility modelling. This includes strict stationarity, mixing, and geometric ergodicity.

  • Account for properties of maximum likelihood estimators in volatility modelling.

  • Account for properties of Realized Volatility (RV) processes, including continuous-time processes.

  • Account for applications of volatility models, including Value-at-Risk (VaR), option pricing, and forecasting.



  • Analyze stochastic properties (e.g. weak mixing and finite moments) time series proceses, such as AR and ARCH. This includes verifying a drift criterion.

  • Show that the likelihood-based estimators are asymptotically normal, and clarify under what conditions such a property holds.

  • Implement the estimation of volatility models.

  • Implement the estimation of volatility in relation to for example VaR analysis, forecasting, and option pricing.

  • Analyze the properties of continuous time processes and show how to estimate their quadratic variation consistently.

  • Discuss the suitability of a given (G)ARCH, SV, or continuous time process given well-known stylized facts about financial returns.



  • Apply the acquired knowledge and skills in new contexts. For example the student should be able to analyze richer classes of models (such as multidimensional) and carry out estimation of these. Another example is to apply the acquired knowledge when considering linear regression models with financial time series data.

  • Read leading and novel journal articles within financial econometrics.

Lectures, active dialog, hands-on empirical applications, derivations on blackboard, exercise classes, mandatory assignments with theoretical and empirical content, coding and implementation of models and estimation approacthes.

The course will be based on

  • R.S. Pedersen and A. Rahbek (2020), “Lecture notes on Econometric Analysis of Time-Varying Volatility”, University of Copenhagen.


Supplementary reading:

  • S. J. Taylor, Asset Price Dynamics, Volatility and Prediction, Princeton University Press, 2007 or 2005 edition (ISBN: 9781400839254), as well as lecture notes handed out during term. 


Various journal articles.

The knowldege obtained from a course as "Econometrics II", Studies of Economics, University of Copenhagen, or from an equivalent course on introductory time series analysis, followed before or parallel to taking "Financial Econometrics A"

In particular, the student should be familiar with:
1. Linear time series models, such as AR and ARMA.
2. Likelihood-based estimation of linear time series models, including the basic properties of the estimators.
3. Basic misspecification tests in time series models (tests for no-autocorrelation, no-ARCH, and normality).

2 hours lectures 1 to 2 times a week from week 36 to 50 (except week 42).
2 hours exercise classes a week from week 36/37 to 50 (except week 42).

The overall schema for the BA 3rd year and Master can be seen at KUnet:
MSc in Economics => "Courses and teaching" => "Planning and overview" => "Your timetable"
BA i Økonomi/KA i Økonomi => "Kurser og undervisning" => "Planlægning og overblik" => "Dit skema"

Timetable and venue:
To see the time and location of lectures and exercise classes please press the link/links under "Timetable"/​"Se skema" at the right side of this page. E means Autumn. The lectures is shown in each link.

You can find the similar information partly in English at
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-E24; [Name of course]””
-Select Report Type: “List – Weekdays”
-Select Period: “Efterår/Autumn”
Press: “ View Timetable”

Please be aware:
- The study administration allocates the students to the exercise classes according to the principles stated in the KUnet.
- If too many students have wished a specific class, students will be registered randomly at another class.
- It is not possible to change class after the second registration period has expired.
- If there is not enough registered students or available teachers, the exercise classes may be jointed.
- The student is not allowed to participate in an exercise class not registered.
- The teacher of the exercise class cannot correct assignments from other students than the registered students in the exercise class except with group work across the classes.
- All exercise classes are taught in English and it is expected that the students ask questions in English, so foreign students are included in the dialog.
- The schedule of the lectures and the exercise classes can change without the participants´ acceptance. If this occur, 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 at 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.



Feedback is obtained throughout the semester by:

  • the lecturer answering questions in class,
  • the lecturer giving oral feedback on written questions from groups,
  • the teaching assistant giving oral feedback on written exercises in exercise classes.
7,5 ECTS
Type of assessment
On-site written exam, 3 hours under invigilation
Type of assessment details
ITX-exam in the exam venues of the university.
The exam assignment is given in English and must be answered in English.
Exam registration requirements

To qualify for the exam the student must no later than the given deadline during the course

  • hand in and have approved 2 out of 3 mandatory assignments.



No aids allowed at the written ITX-exam.

Marking scale
7-point grading scale
Censorship form
No external censorship
at the written exam. The ITX-exam may be chosen for external censorship by random check.
Exam period


Exam information:

The exact time and place will be available in Digital Exam from the middle of the semester. 

More information about examination, rules, aids etc. at Master(UK), Master(DK) and Bachelor(DK).



Same as the ordinary exam. 

You must hand in and have approved 2 our of 3 mandatory assignments for qualifying to the reexam. 


Reexam info:

Exact day, time and place is available in Digital Exam in February. 


More info: Master(UK), Master(DK) and Bachelor

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.


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. Including the ability to analyze the stochastic properties of a time serie processes and describe how a given model should be estimated.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 42
  • Class Instruction
  • 28
  • Preparation
  • 133
  • Exam
  • 3
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 semester

- 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)

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
  • Rasmus Søndergaard Pedersen   (3-7677744469677372326f7932686f)
  • Anders Rahbek   (13-6370666774753074636a64676d4267657170306d7730666d)

See 'Course Coordinators'

Teachers of excersice classes:
Exercise class 1:
Exercise class 2:

Please read "Remarks" regarding the schedule of the teaching.

Saved on the 17-05-2024

Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students