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Title:

MCMC Estimation of the COGARCH(1,1) Model

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This paper presents a Markov chain Monte Carlo (MCMC)-based estimation procedure for the COGARCH(1,1) model driven by a compound Poisson process. The COGARCH model is a continuous-time analogue to the discrete-time GARCH model and captures many of the stylized facts of financial time series, as has been shown in various papers. Principles for th...

This paper presents a Markov chain Monte Carlo (MCMC)-based estimation procedure for the COGARCH(1,1) model driven by a compound Poisson process. The COGARCH model is a continuous-time analogue to the discrete-time GARCH model and captures many of the stylized facts of financial time series, as has been shown in various papers. Principles for the estimation of point processes by MCMC are adapted to the special structure of the COGARCH(1,1) model. The algorithm uses discrete GARCH-type equations on a random grid which changes in each iteration of the MCMC sampler. Moreover, exact solutions of the volatility SDE of the COGARCH(1,1) model are available on this grid, so that no approximations of the COGARCH equations are necessary. The method is also applicable to irregularly spaced observations. A simulation study illustrates the quality of the MCMC estimates. Finally we fit the COGARCH(1,1) model to high-frequency data of the S&P500. Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press. Minimize

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Title:

Modeling individual migraine severity with autoregressive ordered probit models

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Bayes factor, Deviance, Ordinal valued time series, Markov Chain Monte Carlo (MCMC), Proportional odds, Regression

Bayes factor, Deviance, Ordinal valued time series, Markov Chain Monte Carlo (MCMC), Proportional odds, Regression Minimize

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article

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Title:

A Bayesian analysis of market information linkages among NAFTA countries using a multivariate stochastic volatility model

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North American Free Trade Agreement (NAFTA), Information and Volatility Linkages, Volatility Correlations, Markov Chain Monte Carlo, Equity Market Returns, C11, C32, F13

North American Free Trade Agreement (NAFTA), Information and Volatility Linkages, Volatility Correlations, Markov Chain Monte Carlo, Equity Market Returns, C11, C32, F13 Minimize

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article

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Title:

Bayesian Estimation of Lévy Copulas for Multivariate Operational Risks

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operational risk Among the advanced measurement approaches (AMA) of Basel II [1] for calculating capital charges for operational risks, perhaps the most popular in the financial service industry is the loss distribution approach (LDA). Let us briefly focus on one-dimensional operational risk modelling before we move on to the multivariate proble...

operational risk Among the advanced measurement approaches (AMA) of Basel II [1] for calculating capital charges for operational risks, perhaps the most popular in the financial service industry is the loss distribution approach (LDA). Let us briefly focus on one-dimensional operational risk modelling before we move on to the multivariate problem. Consider a single cell (business line / loss event type) for which the total operational loss up to time horizon t is given by the aggregate loss process N(t) S(t) = Xk, t ≥ 0, (1.1) k=1 where (Xk)k∈N is a sequence of independent and identically distributed (i.i.d.) positive random variables and (N(t))t≥0 is a counting process in the time interval [0, t], independent of (Xk)k∈N. The success of LDA models is, at least partially, owing to the fact that they allow for a very intuitive interpretation. Basically, a bank’s total operational loss, e.g. within a given year, is simply the sum of all loss events observed during the year where, of Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-10-12

Source:

http://www-m4.ma.tum.de/Papers/Mueller/fire29.pdf

http://www-m4.ma.tum.de/Papers/Mueller/fire29.pdf Minimize

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text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Limit Experiments of GARCH

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GARCH is one of the most prominent nonlinear time series models, both widely applied and thoroughly studied. Recently, it has been shown that the COGARCH model, which has been introduced a few years ago by Klüppelberg, Lindner and Maller, and Nelson’s diffusion limit are the only functional continuous-time limits of GARCH in distribution. In con...

GARCH is one of the most prominent nonlinear time series models, both widely applied and thoroughly studied. Recently, it has been shown that the COGARCH model, which has been introduced a few years ago by Klüppelberg, Lindner and Maller, and Nelson’s diffusion limit are the only functional continuous-time limits of GARCH in distribution. In contrast to Nelson’s diffusion limit, COGARCH reproduces most of the stylized facts of financial time series. Since it has been proved, that Nelson’s diffusion is not asymptotically equivalent to GARCH in deficiency, we investigate in the present paper the relation between GARCH and COGARCH in Le Cam’s framework of statistical equivalence. We show that GARCH converges generically to COGARCH, even in deficiency, provided that the volatility processes are observed. Hence, from a theoretical point of view, COGARCH can indeed be considered as a continuous-time equivalent to GARCH. Otherwise, when the observations are incomplete, GARCH still has a limiting experiment which we call MCOGARCH, and which is not equivalent, but nevertheless quite similar to COGARCH. In the COGARCH model, the jump times can be more random, as for the MCOGARCH, a fact practitioners may see as an advantage of COGARCH. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-05-02

Source:

http://www-m4.ma.tum.de/Papers/Mueller/GARCHLimits6Preprint.pdf

http://www-m4.ma.tum.de/Papers/Mueller/GARCHLimits6Preprint.pdf Minimize

Document Type:

text

Language:

en

DDC:

330 Economics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Carlo · Minimum Variance Portfolio · Stochastic Volatility · Value at Risk · Volatility Correlations JEL classification:

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Although the idea of a common European currency can be traced back to about 1970, the first major step towards this common currency was made on July 1, 1990, when restrictions on trade and movement of capital were lifted between the members of the

Although the idea of a common European currency can be traced back to about 1970, the first major step towards this common currency was made on July 1, 1990, when restrictions on trade and movement of capital were lifted between the members of the Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-03-30

Source:

http://www-m4.ma.tum.de/Papers/Mueller/euro5.pdf

http://www-m4.ma.tum.de/Papers/Mueller/euro5.pdf Minimize

Document Type:

text

Language:

en

Subjects:

European Monetary Union · European Currencies · Markov Chain Monte

European Monetary Union · European Currencies · Markov Chain Monte Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Stochastic Volatility Models for Ordinal Valued Time Series with Application to Finance

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In this paper we introduce two stochastic volatility models where the response variable takes on only finite many ordered values. Corresponding time series occur in high-frequency finance when the stocks are traded on a coarse grid. For parameter estimation we develop an e#cient Grouped Move Multigrid Monte Carlo (GM-MGMC) sampler. We apply both...

In this paper we introduce two stochastic volatility models where the response variable takes on only finite many ordered values. Corresponding time series occur in high-frequency finance when the stocks are traded on a coarse grid. For parameter estimation we develop an e#cient Grouped Move Multigrid Monte Carlo (GM-MGMC) sampler. We apply both models to price changes of the IBM stock in January, 2001 at the NYSE. Dependencies of the price change process on covariates are quantified and compared with theoretical considerations on such processes. We also investigate whether this data set requires modeling with a heavy-tailed Student-t distribution. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-10-06

Source:

http://www-m4.ma.tum.de/m4/Papers/Czado/OSV2005.pdf

http://www-m4.ma.tum.de/m4/Papers/Czado/OSV2005.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Grouped move ; High-frequency finance ; Markov chain Monte Carlo ; Multigrid Monte Carlo ; Price process

Grouped move ; High-frequency finance ; Markov chain Monte Carlo ; Multigrid Monte Carlo ; Price process Minimize

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Preprint of the corresponding article in Journal of Financial Econometrics (2010) 8 (4) 481-510.

Description:

MCMC estimation of the COGARCH(1,1) model

MCMC estimation of the COGARCH(1,1) model Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-03-30

Source:

http://www-m4.ma.tum.de/Papers/Mueller/coga18.pdf

http://www-m4.ma.tum.de/Papers/Mueller/coga18.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Bayesian inference ; compound Poisson ; continuous time GARCH process ; Lévy process ; volatility estimation

Bayesian inference ; compound Poisson ; continuous time GARCH process ; Lévy process ; volatility estimation Minimize

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Title:

Stochastic Volatility Models for Ordinal Valued Time Series with Application to Finance

Description:

In this paper we introduce a new class of models, called OSV, by combining an ordinal response model and the idea of stochastic volatility. Corresponding time series occur in high-frequency finance when the stocks are traded on a coarse grid. For parameter estimation we develop an efficient Grouped Move Multigrid Monte Carlo (GM-MGMC) sampler. T...

In this paper we introduce a new class of models, called OSV, by combining an ordinal response model and the idea of stochastic volatility. Corresponding time series occur in high-frequency finance when the stocks are traded on a coarse grid. For parameter estimation we develop an efficient Grouped Move Multigrid Monte Carlo (GM-MGMC) sampler. This sampler is based on a scale transformation group, whose elements operate on the random samples of a certain conditional distribution. Also volatility estimates are provided. For illustration, we apply our new model class to price changes of the IBM stock. Dependencies on covariates are quantified and compared with theoretical results for such processes. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-02-18

Source:

http://www-m4.ma.tum.de/m4/Papers/Czado/osv6.pdf

http://www-m4.ma.tum.de/m4/Papers/Czado/osv6.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Grouped move ; High-frequency finance ; Markov chain Monte Carlo ; Multigrid Monte Carlo ; Price process ; Transformation group

Grouped move ; High-frequency finance ; Markov chain Monte Carlo ; Multigrid Monte Carlo ; Price process ; Transformation group Minimize

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Title:

Estimation of stable CARMA models with an application to electricity spot prices

Description:

We discuss theoretical properties and estimation of continuous-time ARMA (CARMA) processes, which are driven by a stable Lévy process. Such processes are very useful in a continuous-time linear stationary set-up: they have a similar structure as the widely used ARMA models, and provide all advantages of a continuous-time model. As an application...

We discuss theoretical properties and estimation of continuous-time ARMA (CARMA) processes, which are driven by a stable Lévy process. Such processes are very useful in a continuous-time linear stationary set-up: they have a similar structure as the widely used ARMA models, and provide all advantages of a continuous-time model. As an application we consider data from a deregulated electricity market. Here we t a CARMA(2,1) model to spot prices from the Singapore New Electricity Market. The quality of the estimates is assessed in a simulation study. The continuous-time modelling aims at a new pricing methodology for energy derivatives. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-23

Source:

http://www-m4.ma.tum.de/Papers/Klueppelberg/scarma100125.pdf

http://www-m4.ma.tum.de/Papers/Klueppelberg/scarma100125.pdf Minimize

Document Type:

text

Language:

en

Subjects:

CARMA model ; electricity prices ; estimation of CARMA models ; stable CARMA model ; stable Ornstein-Uhlenbeck process ; stable Lévy process

CARMA model ; electricity prices ; estimation of CARMA models ; stable CARMA model ; stable Ornstein-Uhlenbeck process ; stable Lévy process Minimize

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