Semi-parametric expected shortfall forecasting in financial markets

ABSTRACT

Bayesian methods have proved effective for quantile estimation, including for financial Value-at-Risk forecasting. Expected shortfall (ES) is a competing tail risk measure, favoured by the Basel Committee, that can be semi-parametrically estimated via asymmetric least squares. An asymmetric Gaussian density is proposed, allowing a likelihood to be developed, that facilitates both pseudo-maximum likelihood and Bayesian semi-parametric estimation, and leads to forecasts of quantiles, expectiles and ES. Further, the conditional autoregressive expectile class of model is generalised to two fully nonlinear families. Adaptive Markov chain Monte Carlo sampling schemes are developed for the Bayesian estimation. The proposed models are favoured in an empirical study forecasting eight financial return series: evidence of more accurate ES forecasting, compared to a range of competing methods, is found, while Bayesian estimated models tend to be more accurate. However, during a financial crisis period most models perform badly, while two existing models perform best.

KEYWORDS:

• CARE model
• nonlinear
• asymmetric Gaussian distribution
• expected shortfall
• Markovchain Monte Carlo method
• semi-parametric

Acknowledgments

The authors thank the AE and referees for their valuable time and careful, extensive comments to improve the quality of this paper. The authors thank Miss Liou-Yan Lin for her initial empirical work on this project.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Richard Gerlach http://orcid.org/0000-0002-5656-4556

Cathy W. S. Chen http://orcid.org/0000-0001-8727-8168

Additional information

Funding

Richard Gerlach is supported by ARC grants [DP0985505] and [DP1094848]. Cathy W.S. Chen is supported by the Ministry of Science and Technology, Taiwan [MOST 105-2118-M-035-003-MY2].