Multivariate Volatility Models

Multivariate Volatility Models (U of Tampere)

Teacher Lecture notes: Professor Seppo Pynnönen,

Purpose: Introduction to modeling of multivariate conditional volatility with financial applications.

Literature: As references for the lecture notes are used:

Alexander, Carol (2001). Market Models. A Guide to Financial Data Analysis. Wiley, Chater 6--9.
Engle, Robert, F. (2002). Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models. Journal of Business & Economic Statistics, 20, No. 3, 339--350.
Tsay, Rue (2002). Analysis of Financial Time Series. Wiley, Cahpters 3, 8 and 9.

Highly recommended additional reading

Engle, Robert F. (2002). Frontiers in ARCH Models. Journal of Applied Econometrics, 17 No. 5, 425--446. (Available in Word document at Engle's homepage > Research)
"Modelling and Forecasting Financial Volatility", a special issue in Journal of Applied Econometrics, 2002, Vol 17, No. 5.
Walter Ender's RATS Programming Manual

Teaching: Lectures (and demonstrations) 12 hours..

Schedule:

Spring 2003:
Thu, February 13, 12.30--16, ls 2107
Wed, February 19, 10--12, ls 2107, 12--14, Pinninkatu 47 ls 301
Thu, February 27 12--16, ls 2017

Contents: (texts in pdf-format) [last changed]

1. Introduction ( 1 x 2 format) ( 2 x 2 format) [Feb 26, 2003]
2. Multivariate GARCH models ( 1 x 2 format) ( 2 x 2 format) [Feb 26, 2003]
3. Dynamic Conditional Correlation ( 1 x 2 format) ( 2 x 2 format) [May 14, 2004]

Exercises:

Wednesday, February 19, 2003

Exam: Term paper. Deadline April 30, 2003.

Istructions:

Get stock indices for four European stock markets [e.g. UK (FTSE 100) France (CAC 40), Germany (DAX) and Swizerland (SSMI)]. These should be available for examle at http://finance.yahoo.com.

Get weekly data starting from the begining of 1990 (or later if data not available)

Report sample statistics of the returns, including contemporaneous correlations.

Report volatilities (annualized standard deviations)

Make graphs of 52 weeks rolling volatilities and correlations

Estimate single GARCH(1,1) models for each return series (you can ignore the possible return autocorrelations)

Carry out a principal component analysis of the returns and produce the principal component series.

Estimate the orhogonal GARCH (O-GARCH) model for the conditional covarince matrix of the returns. Make graphs of the conditional volatilities and correlations from the O-GARCH analysis, and compare the results with the rolling volatilities and correlations.

Prepare a (short) report (in Finnish, Swedish or English) on the above analyses. The report can be a joint paper by two persons. Write the title and your name(s) on the first page. Send you report by ground mail no later than April 30, 2003 to Prof. Seppo Pynnonen, Dept of Math. and Stat. University of Vaasa, Box 700, 65101 Vaasa.

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