Unified Bayesian conditional autoregressive risk measures using the skew exponential power distribution

Abstract

Conditional Autoregressive Value-at-Risk and Conditional Autoregressive Expectile have become two popular approaches for direct measurement of market risk. Since their introduction several improvements both in the Bayesian and in the classical framework have been proposed to better account for asymmetry and local non-linearity. Here we propose a unified Bayesian Conditional Autoregressive Risk Measures approach by using the Skew Exponential Power distribution. Further, we extend the proposed models using a semiparametric P-Spline approximation answering for a flexible way to consider the presence of non-linearity. To make the statistical inference we adapt the MCMC algorithm proposed in Bernardi et al. (2018) to our case. The effectiveness of the whole approach is demonstrated using real data on daily return of five stock market indices.

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Notes

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    For this reason, while for the \({\mathrm{LR}}_{uc}\) and the \({\mathrm{LR}}_{cc}\) tests we consider the null hypothesis rejected at the 5% level we evaluate the DQ test on a 1% significance level, as in Engle and Manganelli (2004)

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Acknowledgements

The views expressed in this paper are those of the authors and do not involve the responsibility of the Bank of Italy. The authors would like to thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improving the final version of the paper. They would also like to thank the Editors for their generous support during the review process.

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Correspondence to Marco Bottone.

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Bottone, M., Petrella, L. & Bernardi, M. Unified Bayesian conditional autoregressive risk measures using the skew exponential power distribution. Stat Methods Appl (2020). https://doi.org/10.1007/s10260-020-00550-6

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Keywords

  • Bayesian quantile regression
  • Skew exponential power
  • Risk measure
  • Adaptive-MCMC
  • CAViaR model
  • CARE model