Workshop: Advanced Modeling in Finance and Insurance
Time: Mon, September 22, 2008, 16:20-17:10
Speaker: Robert Stelzer
Abstract
ultivariate extensions of two continuous time stochastic volatility models driven by Lévy processes - the Ornstein-Uhlenbeck type and the COGARCH model - are introduced.
First, Ornstein-Uhlenbeck type processes taking values in the positive semi-definite matrices are defined using matrix subordinators (special matrix-valued Lévy processes) and a special class of linear operators. Naturally these processes can be used to describe the random evolvement of a covariance matrix over time and we therefore use them in order to define a multivariate stochastic volatility model for financial data which generalises the popular univariate model introduced by Barndorff-Nielsen and Shephard. For this model we show that the conditional characteristic function can be calculated explicitly and we derive results regarding the second order structure, especially regarding the returns and squared returns. Based upon this we present a GMM estimation scheme and illustrate it with a simple example.
Thereafter, an alternative stochastic volatility model driven only by a single d-dimensional Lévy process - the multivariate COGARCH process - is introduced and analysed. After giving conditions for the finiteness of moments and the existence of stationary distributions for the volatility process, we establish asymptotic second order stationarity and show that the log-returns over consecutive intervals of the same length have the autocovariance structure of an ARMA(1,1) process.
Presentation slides (pdf, 609 KB)
URL: www.ricam.oeaw.ac.at/specsem/sef/events/program/presentation.php
This page was made with 100% valid HTML & CSS - Send comments to Webmaster
Today's date and time is 04/24/24 - 02:45 CEST and this file (/specsem/sef/events/program/presentation.php) was last modified on 12/18/12 - 14:00 CEST