基于ARCH-Expectile方法的VaR和ES尾部风险测量

Abstract

Abstract: Determining contributions to an asset or portfolio of assets risk is an important topic in risk management. A downside risk is of primary concern during the last decade. Value at risk and expected shortfall have become two popular downside risk measurements associated with portfolio of assets. Kuan et al^[1].proposed an expectile-based VaR for various CARE model. In this paper, a linear ARCH-Expectile model is proposed to extend Kuan et al. CARE models by introducing an ARCH effect modeling financial data with heteroscedasticity. Based on the coefficient estimates of the proposed expectile model, not only the contribution to portfolio downside risk of risk factors can be analyzed the magnitude of downside risk can also be evaluated. Meanwhile, a two-step estimating procedure is provided and the asymptotic properties of estimators are extablished. Finally, the proposed method is applied to analysis the risk of a company's stock from three aspects of market liquidity, company fundamentals and micro fundamentals. The empirical results find that the risk factors and their magnitude and direction, which impact on return of the stock, are varying with the level of tail losses.

Key words: expectile, downside financial risk, linear ARCH-expectile, asymmetric least squares

CLC Number:

F830

XIE Shang-yu, YAO Hong-wei, ZHOU Yong. VaR and ES Measurements based on ARCH-Expectile Model[J]. Chinese Journal of Management Science, 2014, 22(9): 1-9.

References

[1] Kuan C, Yeh J, Hsu Y. Assessing value at risk with CARE, the conditional autoregressive expectile models[J]. Journal of Econometrics, 2009, 150(2):261-270.

[2] Artzner P, Delbaen F, Eber J, et al. Coherent measures of risk[J]. Mathematical Finance, 1999, 9(3):203-228.

[3] Acerbi C, Tasche D. On the coherence of expected shortfall[J]. Journal of Banking and Finance, 2002(7), 26, 1487-1503.

[4] Aigner D J, Amemiya T, Poirier D J. On the estimation of production frontiers: Maximum likelihood estimation of the parameters of a discontinuous density function[J]. International Economic Review, 1976, 17, 377-396.

[5] Newey W K, Powell J L. Asymmetric least squares estimation and testing[J]. Econometrica. 1987, 55, 819-847.

[6] Efron B. Regression percentiles using asymmetric squared error Loss[J]. Statistica Sinica, 1991, 1(1):93-125.

[7] Yao, Q, Tong H. Asymmetric least squares regression and estimation: A nonparametric approach. Nonparametric Statistics, 1996, 6(2-3):273-292.

[8] Xie S, Alan W, Zhou Y.A varying-coefficient expectile model for estimating Value at Risk[J].Journal of Business and Economic Statistics, DOI:10.1080/07350015.2014.917979, 2014.

[9] Taylor J W. Estimation value at risk and expected shortfall using expectiles[J]. Journal of Financial Econometrics, 2008, 6(2):231-252.

[10] Tasche D. Measuring sectoral diversification in an asymptotic multifactor framework[J]. Arxiv preprint physics/0505142, 2005.

[11] Tasche D. Capital allocation to business units and sub-portfolios: the Euler principle[J]. Arxiv preprint arXiv:0708.2542, 2007.

[12] Rosen D, Saunders D. Analytical methods for hedging systematic credit risk with linear factor portfolios[J]. Journal of Economic Dynamics and Control, 2009, 33(1):37-52.

[13] Cherny A, Madan D. Coherent measurement of factor risks[J]. Arxiv preprint math/0605062, 2006.

[14] Bonti G, Kalkbrener M, Lotz C, et al. Credit risk concentrations under stress[J]. Journal of Credit Risk, 2006, 2(3):115-136.

[15] Rosen D, Saunders D. Risk factor contributions in portfolio credit risk models[J]. Journal of Banking and Finance, 2010, 34(2):336-349.

[16] Manganelli S, Engle R F A comparison of value-at-risk models in finance. Frankfurt amMain:European Central Bank, 2001.

[17] Cai T, Wang Lie. Adaptive variance function estimation in heteroscedastic nonparametric regression[J]. The Annals of Statistics, 2008, 36(5):2025-2054.

[18] Chen Songxi, Tang Chengyong. Nonparametric inference of value at risk for dependent financial returns[J]. Journal of Financial Econometrics, 2005, 3(2):227-255.

[19] Gourieroux C, Scaillet O, Laurent J P. Sensitivity analysis of values at risk[J]. Journal of Empirical Finance, 2000, 7(3):225-245.

[20] Scaillet O. Nonparametric estimation and sensitivity analysis of expected shortfall[J]. Mathematical Finance, 2004, 14(1):115-129.

[21] Chen, Songxi. Nonparametric estimation of expected shortfall[J]. Journal of Financial Econometrics, 2008, 6(1):87-107.

[22] Diebold F X, Schuermann T, Stroghair J D. Pitfalls and opportunities in the use of extreme value theory in risk management[J]. Journal of Risk Finance 1 (Winter), 2000, 1(2):30-36.

[23] McNeil A J, Frey R. Estiamtion of tail-related risk measures for heteroscedastic financial time series: An extreme value approach[J]. Journal of Empirical Finance, 2000, 7(3):271-300.

[24] McNeil A J, Frey R, Embrechts P. Quantitative risk management[M]. New Jersey: Princeton University Press, 2005.

[25] Jones M C. Expectiles and M-quantiles are quantiles[J]. Statistics and Probability Letters, 1994, 20(2):149-153.

[26] Abdous B, Remillard B. Relating quantiles and expectiles under weighted-symmetry[J]. Annals of the Institute of Statistical Mathematics, 1995, 47(2), 371-384.

[27] 李一红, 吴世农.中国股市流动性溢价的实证研究[J].管理评论, 2003, 15(11):34-42.

[28] 吴文锋, 芮萌, 陈工孟. 中国股票收益的非流动性补偿[J]. 世界经济, 2003, (7):54-60.

[29] 苏冬蔚, 麦元勋. 流动性与资产定价:基于我国股市资产换手率与预期收益的实证研究[J]. 经济研究, 2004, (2).:95-105.

[30] 汪炜, 周宇. 中国股市规模效应和时间效应的实证分析[J]. 经济研究, 2002, (10):16-21.

[31] 张祥建, 谷伟, 郭岚. 上海股票市场规模效应的实证研究及原因探析[J]. 大连理工大学学报, 2003, (4):24-28.

[31] 邵晓阳, 苏敬勤, 于圣睿. 中国A股市场规模效应实证研究[J]. 管理评论, 2004, 16(7):11-15.

VaR and ES Measurements based on ARCH-Expectile Model

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