Efficient Bayesian inference for stochastic time-varying copula models

Almeida, Carlos; Czado, Claudia

doi:10.1016/j.csda.2011.08.015

Cited by 44 publications

(38 citation statements)

References 31 publications

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“…Research in this direction is still at a rather early stage (see Ausin and Lopes (2010), Manner and Reznikova (2012) and Almeida and Czado (2012)). While the present work constitutes one of the first applications of vine copulas in dimensions 50 or higher (and, to the best of our knowledge, is the first to perform joint maximum likelihood estimation in such dimensions), dynamic (vine) copula models in such dimensions are not yet feasible.…”

Section: Discussionmentioning

confidence: 98%

Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50

Brechmann

Czado²

2013

Statistics &Amp; Risk Modeling

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149

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The demand for an accurate financial risk management involving larger numbers of assets is strong not only in view of the financial crisis of 2007-2009. Especially dependencies among assets have not been captured adequately. While standard multivariate copulas have added some flexibility, this flexibility is insufficient in higher dimensional applications. Vine copulas can fill this gap by benefiting from the rich class of existing bivariate parametric copula families. Exploiting this in combination with GARCH models for the margins, we develop a regular vine copula based factor model for asset returns, the Regular Vine Market Sector model, which is motivated by the classical CAPM and shown to be superior to the CAVA model proposed by Heinen and Valdesogo (2009). The model can also be used to separate the systematic and idiosyncratic risk of specific stocks, and we explicitly discuss how vine copula models can be employed for active and passive portfolio management. In particular, Value-at-Risk forecasting and asset allocation are treated in detail. All developed models and methods are used to analyze the Euro Stoxx 50 index, a major market indicator for the Eurozone. Relevant benchmark models such as the popular DCC model and the common Student's t copula are taken into account.

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Section: Discussionmentioning

confidence: 98%

Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50

Brechmann

Czado²

2013

Statistics &Amp; Risk Modeling

Self Cite

149

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“…(2012). We already covered six DGPs that were also analyzed by Almeida and Czado (2012). Instead of running their sampler we make the comparison with respect to these six cases.…”

Section: Methodsmentioning

confidence: 99%

“…There are several points which make the comparison slightly less reliable. First Almeida and Czado (2012) did not report exact computation times but they note that 100 000 iterations of their sampler take about 15 minutes. We use this number to calculate the AESR values from the effective sample sizes they report in their paper.…”

Section: Methodsmentioning

confidence: 99%

“…If we expected higher lower than upper tail dependence we can replace the Gumbel copula by a survival Gumbel copula which has the density c SG (u 1 , u 2 ) = c G (1 − u 1 , 1 − u 2 ). To allow for time variation we use the mixture copula C M of (10) within the dynamic bivariate copula model of Almeida and Czado (2012). A nonlinear state space model for T bivariate random vectors (U t1 , U t2 ) t=1,...,T ∈ [0, 1] T ×2 , corresponding to T time points, is given by…”

Section: Dependence Modelmentioning

confidence: 99%

“…Vatter and Chavez-Demoulin (2015) introduce a bivariate copula model, where the dependence parameter follows a generalized additive model. Another approach is the dynamic bivariate copula model proposed by Almeida and Czado (2012) and Hafner and Manner (2012), which we will analyze within our state space framework. For this model, we consider single parameter copula families for which there is a one-to-one correspondence between the copula parameter, denoted by θ, and Kendall's τ .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Bayesian Inference for Nonlinear State Space Models With Univariate Autoregressive State Equation

Kreuzer

Czado

2020

Journal of Computational and Graphical Statistics

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Latent autoregressive processes are a popular choice to model time varying parameters. These models can be formulated as nonlinear state space models for which inference is not straightforward due to the high number of parameters. Therefore maximum likelihood methods are often infeasible and researchers rely on alternative techniques, such as Gibbs sampling. But conventional Gibbs samplers are often tailored to specific situations and suffer from high autocorrelation among repeated draws. We present a Gibbs sampler for general nonlinear state space models with an univariate autoregressive state equation. For this we employ an interweaving strategy and elliptical slice sampling to exploit the dependence implied by the autoregressive process. Within a simulation study we demonstrate the efficiency of the proposed sampler for bivariate dynamic copula models. Further we are interested in modeling the volatility return relationship. Therefore we use the proposed sampler to estimate the parameters of stochastic volatility models with skew Student t errors and the parameters of a novel bivariate dynamic mixture copula model. This model allows for dynamic asymmetric tail dependence. Comparison to relevant benchmark models, such as the DCC-GARCH or a Student t copula model, with respect to predictive accuracy shows the superior performance of the proposed approach.

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Multivariate option pricing using copulae

Bernard

Czado

2012

Appl Stoch Models Bus & Ind

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The complexity of financial products significantly increased in the past 10 years. In this paper, we investigate the pricing of basket options and more generally of complex exotic contracts depending on multiple indices. Our approach assumes that the underlying assets evolve as dependent GARCH(1, 1) processes. The dependence among the assets is modeled using a copula based on paircopula constructions. Unlike most previous studies on this topic, we do not assume that the dependence observed between historical asset prices is similar to the dependence under the risk-neutral probability. The method is illustrated with US market data on basket options written on two or three international indices.

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Efficient Bayesian inference for stochastic time-varying copula models

Cited by 44 publications

References 31 publications

Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50

Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50

Efficient Bayesian Inference for Nonlinear State Space Models With Univariate Autoregressive State Equation

Multivariate option pricing using copulae

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