# Financial Econometrics A (F)

### Course content

The course gives an introduction to the properties and stylized facts of univariate asset returns and their variability with emphasis on modeling of (conditional) volatility. We consider three different modeling approaches to volatility: (1) GARCH-type models, (2) stochastic volatility models (SV), and (3) realized volatility (RV).

The stochastic properties of the processes are analyzed and discussed in detail using mathematical statistical methods. A key tool for the analysis of GARCH-type and SV models is the so-called drift criterion for Markov chains.

Estimation of volatility and volatility models will be based primarily on (quasi) maximum likelihood. This includes applications of the EM-algorithm as well as the Kalman filter.

The theoretical properties of the estimators are analyzed and sufficient conditions for asymptotic normality are stated and verified.

All estimation is carried out in OxMetrics 7.0 and the students are expected to do some amount of coding using the Ox programming language.

The goodness of fit of the models are discussed based on analysis of the model residuals.

Education

MSc programme in Economics – elective course

Bacheloruddannelsen i økonomiPrioriteret valgfag på 3. år

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

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

MSc programme in mathematics-economics

Learning outcome

After completing the course, the student should be able to:

Knowledge

• 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.

Skills

• 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 (under suitable conditions) that the likelihood-based estimators are asymptotically normal.

• Implement the estimation of volatility models using the Ox language.

• 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.

Competencies

• 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.

Lectures and exercise classes.

The course will be based on 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 Econometrics II before or at the same time the Financial Econometrics A is taken or an equivalent course on introductory time series analysis.
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).

Schedule:
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 can be seen at https:/​/​intranet.ku.dk/​polit_ba/​undervisning/​Lektionsplan-E17/​skemaer/​Sider/​default.aspx

or the Master at https:/​/​intranet.ku.dk/​economics_ma/​courses/​CourseCatalogue-E17/​Courseschema/​Pages/​default.aspx

Timetable and venue:
To see the time and location of lectures and exercise classes please press the link/links under "Se skema" (See schedule) 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
https:/​​​/​​​skema.ku.dk/​​​ku1718/​​​uk/​​​module.htm
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-E17; [Name of course]””
-Select Report Type: “List – Weekdays”
-Select Period: “Efterår/Autumn – Weeks 31-5”
Press: “ View Timetable”

Please be aware regarding exercise classes:
- The schedule of the exercise classes is only a pre-planned schedule and can be changed until just before the teaching begins without the participants accept. If this happens it will be informed at the intranet or can be seen in the app myUCPH and at the above link
- That 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, because the room has only seats for the amount of registered student.
- 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.
- That all exercise classes will be taught in English.

ECTS
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
Individual exam at the computers of Copenhagen University.
The exam assignment is given in English and can be answered in English or in Danish. Language must be chosen at the course or exam registration.
Aid
Without aids
Marking scale
Censorship form
External censorship
if chosen by the Head of Studies.
##### 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 be able to demonstrate in an excellent manner that he or she has acquired and can make use of the knowledge, skills and competencies listed in the learning outcomes.

In order to pass the exam the student is required to demonstrate understanding of the material covered in the course. This may include 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 Exercises
• 28
• Preparation
• 133
• Exam
• 3
• English
• 206