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Estimation of Conditional Weighted Expected Shortfall under Adjusted Extreme Quantile Autoregression
Department of Mathematics, Institute for Basic Sciences, Technology and Innovation, Pan African University, Nairobi, Kenya
Department of Mathematics, Machakos University, Machakos, Kenya
Department of Statistics and Actuarial Sciences, Kenyatta University, Nairobi, Kenya
- 1 Department of Mathematics, Institute for Basic Sciences, Technology and Innovation, Pan African University, Nairobi, Kenya
- 2 Department of Mathematics, Machakos University, Machakos, Kenya
- 3 Department of Statistics and Actuarial Sciences, Kenyatta University, Nairobi, Kenya
Journal of Mathematical Finance·Volume 11 (2021)·Pages 373–385·Published 9 June 2021·DOI10.4236/jmf.2021.113021
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Abstract
In this paper, we present an estimator that improves the well-calibrated coherent risk measure: expected shortfall by restructuring its functional form to incorporate dynamic weights on extreme conditional quantiles used in its definition. Adjusted Extreme Quantile Autoregression will is used in estimating intermediary location measures. Consistency and coherence of the estimator are also proved. The resulting estimator was found to be less conservative compared to the expected shortfall.
KeywordsExreme Quantile AutoregressionExpected ShortfallValue at RiskCoherenceRisk Measurement
- Artzner, P., Delbaen, F., Eber, J.-M. and Heath, D. (1999) Coherent Measures of Risk. Journal of Mathematical Finance, 9, 203-228. https://doi.org/10.1111/1467-9965.00068
- Acerbi, C., Nordio, C. and Sirtori, C. (2001) Expected Shortfall as a Tool for Financial Risk Management. arXiv Preprint cond-mat/0102304.
- Acerbi, C. and Tasche, D. (2002) On the Coherence of Expected Shortfall. Journal of Banking & Finance, 26, 1487-1503. https://doi.org/10.1016/S0378-4266(02)00283-2
- Roccioletti, S. (2015) Backtesting Value at Risk and Expected Shortfall. Springer. https://doi.org/10.1007/978-3-658-11908-9
- Basel Committee on Banking Supervision (2013) Consultative Document—Fundamental Review of the Trading Book: A Revised Market Risk Framework (tech. rep.). https://www.bis.org/publ/bcbs265.pdf
- Gneiting, T. (2011) Making and Evaluating Point Forecasts. Journal of the American Statistical Association, 106, 746-762. https://doi.org/10.1198/jasa.2011.r10138
- Acerbi, C. and Szekely, B. (2014) Back-Testing Expected Shortfall. Risk, 27, 76-81.
- Cont, R., Deguest, R. and Scandolo, G. (2010) Robustness and Sensitivity Analysis of Risk Measurement Procedures. Quantitative Finance, 10, 593-606. https://doi.org/10.1080/14697681003685597
- Peracchi, F. and Tanase, A.V. (2008) On Estimating the Conditional Expected Shortfall. Applied Stochastic Models in Business and Industry, 24, 471-493. https://doi.org/10.1002/asmb.729
- Leorato, S., Peracchi, F. and Tanase, A.V. (2012) Asymptotically Efficient Estimation of the Conditional Expected Shortfall. Computational Statistics & Data Analysis, 56, 768-784. https://doi.org/10.1016/j.csda.2011.02.020
- Kithinji, M.M., Mwita, P.N. and Kube, A.O. (2021) Adjusted Extreme Conditional Quantile Autoregression with Application to Risk Measurement. Journal of Probability and Statistics, 2021, Article ID: 6697120. https://doi.org/10.1155/2021/6697120
- Acerbi, C. (2002) Spectral Measures of Risk: A Coherent Representation of Subjective Risk Aversion. Journal of Banking & Finance, 26, 1505-1518. https://doi.org/10.1016/S0378-4266(02)00281-9
- Whitt, W. (1980) Some Useful Functions for Functional Limit Theorems. Mathematics of Operations Research, 5, 67-85. https://doi.org/10.1287/moor.5.1.67
- Embrechts, P. and Wang, R. (2015) Seven Proofs for the Subadditivity of Expected Shortfall. Dependence Modeling, 3, 126-140. https://doi.org/10.1515/demo-2015-0009