[Forside] [Hovedområder] [Perioder] [Udannelser] [Alle kurser på en side]
LEARNING OBJECTIVES:
After having followed the course the students should be able:
• to describe and explain various univariate and multivariate GARCH models
• to describe and apply likelihood based estimation of univariate and multivariate GARCH models
• to relate the application of the theoretical concepts discussed in the lectures to practical financial decision problems
• to describe the notion of Brownian motion and to explain its sample path properties
• to describe and reflect on the concept of quadratic variation of (jump) diffusions and to relate it to volatility measurement
• to describe the main ideas of the theory underlying stochastic integration with respect to Brownian motion and of the Itô formula
• to describe some well-known stochastic volatility models, such as Heston, constant elasticity of variance (CEV) and Barndorff-Nielsen and Shephard models
• to formulate simulation procedures for GARCH and stochastic volatility models
• to derive, analyze and apply the concept of realized variance and its multivariate extension
• analyze the role and impact of market microstructure on the practical application of realized variance models.
COURSE DESCRIPTION:
The main aim of the course is to provide a theoretical and empirical treatment of the modeling and analysis of financial market volatility.
The theory will include models for daily as well as high frequency data, univariate and multivariate approaches, continuous time and discrete time setups. Within each topic, we will present the standard approaches and extend the theory to give insights into the latest developments in the field.
The theoretical part of the course will be complemented by empirical applications in the fields of risk management, portfolio management and asset pricing. At the end of the course each participant is expected to write a small paper on one of the topics covered in the course.
COURSE SUBJECT AREAS:
1. Univariate GARCH models
Tsay (2002), Chapter 3.1 - 3.7 (28 pages)
2. Multivariate GARCH models
Tsay (2002), Chapters 9.1 - 9.3 (19 pages), Bauwens L., S. Laurent, and J. Rombouts (2006), "Multivariate GARCH models: a survey", Journal of Applied Econometrics, 21, 79 - 109 (29 pages)
3. Introduction to continuous time stochastic processes
Tsay (2002), Chapter 6 (30 pages)
4. Realized Variance and Covariation
Barndorff-Nielsen, O. E. & Shephard, N. (2002), ‘Econometric analysis of realised volatility and its use in estimating stochastic volatility models', Journal of the Royal Statistical Society, B 64, 253 - 280. (27 pages)
Barndorff-Nielsen, O. E. & Shephard, N. (2004a), ‘Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics', Econometrica 72, 885 - 925 (40 pages)
5. Market Microstructure and Volatility Estimation
Hansen and Lunde (2006) "Realized Variance and Market Microstructure Noise.", Journal of Economic and Business Statistics, 24, 127 - 161 (34 pages)
Ait-Sahalia, Mykland, Zhang (2005), "A tale of two time scales: Determining integrated volatility with noisy high-frequency data.", Journal of the American Statistical Association, 100, 1394 - 1411 (17 pages)
Hayashi and Yoshida (2005), "On Covariance Estimation of Non-Synchronously Observed Diffusion Processes.", Bernoulli, 11, 359-379 (20 pages)
6. Volatility Estimation and Jumps
Barndorff-Nielsen, O. E. & Shephard, N. (2006), "Econometrics of testing for jumps in financial economics using bipower variation.", Journal of Financial Econometrics 4, 1 - 30. (30 pages).
REQUIRED COURSES:
7020 Econometrics.
LECTURERS:
Almut Veraart and Valeri Voev.
TEACHING METHOD:
Classroom lectures with theoretical and computer exercises integrated in lectures. Additional ad-hoc project-related teaching assistance will be offered.
LITERATURE:
• Tsay, R. S. (2002): Analysis of Financial Time Series: Financial Econometrics, Wiley, New York (77 pages).
• Lecture materials which will be posted on the course web page (100 pages).
• Articles (197 pages).
Additional literature (optional):
• Cont, R. & P. Tankov (2004): Financial Modelling with Jump Processes, Chapman & Hall, New York.
Total number of pages: 77 pages (Tsay) + 197 pages (articles) + 100 pages (lecture materials) = 374 pages.
FORM OF ASSESSMENT:
Oral exam based on project report (ca. 30 min with a 10 min presentation and ca. 20 min discussion).
EXAMINATION AIDS ALLOWED: Only, the written project report.
