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


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.

Restrictions due to Coronavirus:
The teaching in this course may be changed to be taught either fully or partly online due to COVID-19. For further information, please see the course room on Absalon (for enrolled students).

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-E21; [Name of course]””
-Select Report Type: “List – Weekdays”
-Select Period: “Efterår/Autumn”
Press: “ View Timetable”

Please be aware:
- The schedule of the exercise classes is only a pre-planned schedule and can be changed until the teaching begins without the participants´ acceptance. If this happens you can see the new schedule in your personal timetable at KUnet, in the app myUCPH and through the links in the right side and the link above.
- 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 will be taught in English.
- It is the students´s own responsibility to continuously update themselves about their studies, their teaching, their schedule, their exams etc. through the curriculum of the study programmes, the study pages at KUnet, student messages, the course descriptions, 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
Written examination, 3 hours under invigilation
as an ITX-exam in the exam venues of the university.

The exam assignment is given in English and must be answered in English.

Changes due to Coronavirus:
In the event that COVID-19 restrictions may affect the conduction of the ITX-exams, the written exam and the re-sit exam will be changed to a take-home exam with all aids. If done so, the changes will be announced in study messages at KUnet, in the Digital Exam portal and here in the Exam section of the course description.

The take-home exams will still be individual and it is not allowed to communicate with any one about the exam assignment nor the solution at all. It is also prohibited to distribute data and other information at all. If this or alike actions happens, it will be regarded as cheating and plagiarism.

No aids allowed at the written ITX-exams.


If the ITX-exams are changed to take-home exams due to COVID-19, the written take-home exams will be with all aids.


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
at the written exams. The ITX-exam may be chosen for external censorship by random check.

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.


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