Bayesian Tail Risk Interdependence Using Quantile Regression

Bernardi, Mauro; Gayraud, Ghislaine; Petrella, Lea

doi:10.1214/14-ba911

Cited by 44 publications

(33 citation statements)

References 61 publications

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“…See, e.g Geraci and Bottai (2007), Koenker (2004), Koenker (2017), Marino and Farcomeni (2015) for references. Bayesian versions of quantile regression have also been extensively proposed (see Yu and Moyeed (2001), Kottas and Gelfand (2001), Kottas and Krnjajic (2009), Bernardi et al (2015)). It is well known in the literature that the univariate quantile regression approach has a direct link with the Asymmetric Laplace (AL) distribution.…”

Section: Introductionmentioning

confidence: 99%

Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress

Petrella

Raponi

2019

Journal of Multivariate Analysis

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This paper proposes a maximum-likelihood approach to jointly estimate marginal conditional quantiles of multivariate response variables in a linear regression framework.We consider a slight reparameterization of the Multivariate Asymmetric Laplace distribution proposed by Kotz et al (2001) and exploit its location-scale mixture representation to implement a new EM algorithm for estimating model parameters. The idea is to extend the link between the Asymmetric Laplace distribution and the well-known univariate quantile regression model to a multivariate context, i.e. when a multivariate dependent variable is concerned. The approach accounts for association among multiple responses and study how the relationship between responses and explanatory variables can vary across different quantiles of the marginal conditional distribution of the responses. A penalized version of the EM algorithm is also presented to tackle the problem of variable selection. The validity of our approach is analyzed in a simulation study, where we also provide evidence on the efficiency gain of the proposed method compared to estimation obtained by separate univariate quantile regressions. A real data application is finally proposed to study the main determinants of financial distress in a sample of Italian firms.

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Section: Introductionmentioning

confidence: 99%

Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress

Petrella

Raponi

2019

Journal of Multivariate Analysis

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“…From the equations given in (12) and the priors defined in Section 2.2.2, we follow Bernardi et al [15] to derive the full conditional distributions of = ( 1 , . .…”

Section: Full Conditional Distributionsmentioning

confidence: 99%

“…They also showed that the Bayesian approach yields a proper full conditional distribution, even for an improper uniform prior on the quantile coefficients and they used the Metropolis-Hastings algorithm for implementation. Further, Kozumi and Kobayashi [14] and Bernardi et al [15] considered that the scale parameter of the ALD is unknown. They used the location-scale mixture representation of the ALD, which enables developing a Gibbs sampling algorithm for the Bayesian quantile regression model.…”

Section: Introductionmentioning

confidence: 99%

Fully Bayesian Estimation of Simultaneous Regression Quantiles under Asymmetric Laplace Distribution Specification

Bleik

2019

Journal of Probability and Statistics

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In this paper, we are interested in estimating several quantiles simultaneously in a regression context via the Bayesian approach. Assuming that the error term has an asymmetric Laplace distribution and using the relation between two distinct quantiles of this distribution, we propose a simple fully Bayesian method that satisfies the noncrossing property of quantiles. For implementation, we use Metropolis-Hastings within Gibbs algorithm to sample unknown parameters from their full conditional distribution. The performance and the competitiveness of the underlying method with other alternatives are shown in simulated examples.

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“…In this paper, we show using a non-convex risk measure, VaR, will result in a hedging method that is based on quantile regression. For quantile regression in particular, there are lots of interesting approaches developed in practice and theory that can decrease the computational cost see for example Yu and Moyeed (2001), Koenker (2005) and Bernardi et al (2015) .…”

Section: Corollarymentioning

confidence: 99%

A Robust Approach to Hedging and Pricing in Imperfect Markets

Assa

Gospodinov

2017

Risks

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Abstract:This paper proposes a model-free approach to hedging and pricing in the presence of market imperfections such as market incompleteness and frictions. The generality of this framework allows us to conduct an in-depth theoretical analysis of hedging strategies with a wide family of risk measures and pricing rules, and study the conditions under which the hedging problem admits a solution and pricing is possible. The practical implications of our proposed theoretical approach are illustrated with an application on hedging economic risk.

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Bayesian Tail Risk Interdependence Using Quantile Regression

Cited by 44 publications

References 61 publications

Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress

Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress

Fully Bayesian Estimation of Simultaneous Regression Quantiles under Asymmetric Laplace Distribution Specification

A Robust Approach to Hedging and Pricing in Imperfect Markets

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