基于时变极值方法的VaR预测模型以及应用

doi:10.16381/j.cnki.issn1003-207x.2022.1541

Abstract

Abstract:

VaR is an important tool for risk management. This paper proposes a time-varying extreme VaR prediction model based on high frequency data， namely ARFIMA-RGARCH-DPOT-VAR model. Based on the basic mean-variance model， the model assumes that return fluctuations are affected by extreme values that obey generalized Pareto （GP） distributions， and GP dynamic parameters are driven by realized volatility measures. The model is modeled and estimated based on the two-step method. First， the ARFIMA-RGARCH model is used to model the return sequence and the standardized innovation is obtained. Secondly， the realized fluctuation measure predicted by RGARCH model is taken as the covariable， and the distribution parameters of POT with standardized innovation exceeding the threshold are estimated dynamically. On this basis， the prediction of VaR is realized. In the empirical analysis， the VaR prediction results of three major indexes in China's stock market and the USA’s stock market， namely Shanghai Composite Index， CSI 300 Index， Shenzhen Composite Index， S&P500 Index and Nasdaq Index show that the RGARCH-DPOT method proposed by us is more accurate than the standard RGARCH model and HEAVY model in predicting tail risks.

Key words: VaR predicting, RGARCH, extreme theory, POT, realized volatility

CLC Number:

F830.9

Shijia Song, Fei Tian, Handong Li. VaR Prediction Model Based on Time-varying Extremum Method and Its Application[J]. Chinese Journal of Management Science, 2025, 33(2): 61-70.

Figures/Tables 5

$α$		99.50%			99%			98%
指数	模型	$p U C$	$p C C$	$p D Q$	$p U C$	$p C C$	$p D Q$	$p U C$	$p C C$	$p D Q$
上证指数	ARFIMA-RGARCH	0.0021	0.0086	0.0024	0.031	0.0754	0.0097	0.6031	0.8432	0.412
	ARFIMA-RGARCH-DPOT	0.2932	0.545	0.998	0.7792	0.732	0.998	0.4044	0.6993	0.252
	HEAVY	0.0001	0.0002	0.123	0.0023	0.0045	0.2344	0.2336	0.3466	0.7796
沪深300	ARFIMA-RGARCH	0.0106	0.0144	0.0001	0.0617	0.1501	0.0101	0.4011	0.6832	0.1988
	ARFIMA-RGARCH-DPOT	0.0889	0.192	0.8923	0.2034	0.1992	0.2002	0.411	0.701	0.5798
	HEAVY	0.0002	0.0003	0.7765	0.0055	0.0068	0.7965	0.3345	0.4565	0.663
深证成指	ARFIMA-RGARCH	0.052	0.0535	0.0002	0.0329	0.1103	0.0419	0.3206	0.5324	0.16
	ARFIMA-RGARCH-DPOT	0.2012	0.355	0.9998	0.398	0.4823	0.543	0.654	0.7312	0.0472
	HEAVY	0.0002	0.0004	0.8773	0.0095	0.0122	0.6445	0.2232	0.543	0.6635
标普500	ARFIMA-RGARCH	0.0432	0.0342	0.0001	0.0278	0.0678	0.0564	0.3445	0.4201	0.187
	ARFIMA-RGARCH-DPOT	0.3321	0.4523	0.6379	0.2679	0.298	0.4023	0.3187	0.4326	0.5889
	HEAVY	0.0102	0.0203	0.7793	0.0432	0.0504	0.7793	0.2245	0.2987	0.988
纳斯达克	ARFIMA-RGARCH	0.0498	0.0431	0.0001	0.0673	0.0886	0.0587	0.3024	0.3637	0.1662
	ARFIMA-RGARCH-DPOT	0.3014	0.4983	0.6325	0.3797	0.3079	0.4565	0.3668	0.4236	0.8024
	HEAVY	0.0153	0.0288	0.8556	0.0432	0.0504	0.694	0.2663	0.323	0.988
$α$		97%			96%			95%
指数	模型	$p U C$	$p C C$	$p D Q$	$p U C$	$p C C$	$p D Q$	$p U C$	$p C C$	$p D Q$
上证指数	ARFIMA-RGARCH	0.861	0.522	0.6789	0.5202	0.455	0.823	0.11	0.0751	0.6014
	ARFIMA-RGARCH-DPOT	0.5798	0.5408	0.554	0.6985	0.8876	0.4435	0.8123	0.8456	0.389
	HEAVY	0.532	0.5543	0.6233	0.7732	0.7963	0.9445	0.779	0.8996	0.988
沪深300	ARFIMA-RGARCH	0.686	0.423	0.154	0.412	0.4088	0.4102	0.1616	0.3128	0.4123
	ARFIMA-RGARCH-DPOT	0.802	0.5094	0.9473	0.556	0.6987	0.654	0.843	0.5998	0.2115
	HEAVY	0.663	0.6998	0.8864	0.7749	0.856	0.7855	0.793	0.8865	0.9554
深证成指	ARFIMA-RGARCH	0.3201	0.5981	0.2885	0.6932	0.7533	0.6102	0.3284	0.6155	0.2102
	ARFIMA-RGARCH-DPOT	0.8043	0.5034	0.3324	0.7887	0.6884	0.269	0.755	0.8235	0.0055
	HEAVY	0.8445	0.897	0.6659	0.6885	0.7232	0.554	0.8974	0.8225	0.9554
标普500	ARFIMA-RGARCH	0.2993	0.312	0.3224	0.5023	0.5864	0.455	0.566	0.5889	0.586
	ARFIMA-RGARCH-DPOT	0.432	0.4558	0.5664	0.5885	0.6985	0.8565	0.6639	0.553	0.1545
	HEAVY	0.663	0.6998	0.9045	0.7325	0.7885	0.897	0.7795	0.72	0.8765
纳斯达克	ARFIMA-RGARCH	0.3125	0.3326	0.266	0.5568	0.6332	0.668	0.5021	0.5212	0.498
	ARFIMA-RGARCH-DPOT	0.4565	0.4698	0.733	0.6125	0.7025	0.7665	0.512	0.6645	0.1443
	HEAVY	0.5435	0.6375	0.9045	0.7732	0.798	0.8856	0.798	0.856	0.988

$α$		99.5%	99%	98.5%	98%	97.5%
指数	模型	排序	排序	排序	排序	排序
上证指数	ARFIMA-RGARCH-DPOT	1	1	1	1	1
	ARFIMA-RGARCH	淘汰2	淘汰2	淘汰2	淘汰2	淘汰2
	HEAVY	淘汰3	淘汰3	淘汰3	淘汰3	淘汰3
	$p M C S$	0.012	0.032	0.055	0.02	0.068
沪深300	ARFIMA-RGARCH-DPOT	1	1	1	1	1
	ARFIMA-RGARCH	2	淘汰2	淘汰2	淘汰2	淘汰2
	HEAVY	淘汰3	淘汰3	淘汰3	淘汰3	淘汰3
	$p M C S$	0.0206	0.079	0.0604	0.0584	0.062
深证成指	ARFIMA-RGARCH-DPOT	1	1	1	1	1
	ARFIMA-RGARCH	淘汰2	淘汰2	淘汰2	2	淘汰2
	HEAVY	淘汰3	淘汰3	淘汰3	淘汰3	淘汰3
	$p M C S$	0.182	0.083	0.025	0.012	0.01
标普500	ARFIMA-RGARCH-DPOT	1	1	1	1	1
	ARFIMA-RGARCH	2	淘汰2	淘汰2	2	淘汰2
	HEAVY	淘汰3	淘汰3	淘汰3	淘汰3	淘汰3
	$p M C S$	0.037	0.014	0.22	0.048	0.064
纳斯达克	ARFIMA-RGARCH-DPOT	1	1	1	1	1
	ARFIMA-RGARCH	淘汰2	淘汰2	淘汰2	淘汰2	淘汰2
	HEAVY	淘汰3	淘汰3	淘汰3	淘汰3	淘汰3
	$p M C S$	0.066	0.146	0.087	0.014	0.255
$α$		97%	96.5%	96%	95.5%	95%
指数	模型	排序	排序	排序	排序	排序
上证指数	ARFIMA-RGARCH-DPOT	1	2	2	淘汰2	淘汰2
	ARFIMA-RGARCH	淘汰2	1	1	1	1
	HEAVY	淘汰3	3	淘汰3	淘汰3	淘汰3
	$p M C S$	0.014	0.6336	0.0362	0.0426	0.0093
沪深300	ARFIMA-RGARCH-DPOT	1	2	2	淘汰2	淘汰2
	ARFIMA-RGARCH	淘汰2	1	1	1	1
	HEAVY	淘汰3	淘汰3	淘汰3	淘汰3	淘汰3
	$p M C S$	0.054	0.2388	0.0109	0.034	0.024
深证成指	ARFIMA-RGARCH-DPOT	1	1	2	2	2
	ARFIMA-RGARCH	淘汰2	2	1	1	1
	HEAVY	淘汰3	3	淘汰3	淘汰3	淘汰3
	$p M C S$	0.04	0.0388	0.0235	0.027	0.0197
标普500	ARFIMA-RGARCH-DPOT	1	2	2	2	2
	ARFIMA-RGARCH	2	1	1	1	1
	HEAVY	淘汰3	淘汰3	淘汰3	淘汰3	淘汰3
	$p M C S$	0.028	0.014	0.048	0.015	0.007
纳斯达克	ARFIMA-RGARCH-DPOT	1	2	2	2	淘汰2
	ARFIMA-RGARCH	淘汰2	1	1	1	1
	HEAVY	淘汰3	淘汰3	淘汰3	淘汰3	淘汰3
	$p M C S$	0.102	0.025	0.034	0.038	0.156

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标准差	偏度	超额峰度	ADF检验		长记忆性检验		ARCH检验
标准差	偏度	超额峰度	Dickey-Fuller	p值	Q(50)	p值	Q(12)	p值
0.01600	0.58884	4.98347	-13.9433	<0.01	117.55	2.3e-7	942.03	<2.2e-16
0.01719	0.50860	4.08856	-13.6651	<0.01	116.02	3.64e-7	955.14	<2.2e-16
0.01851	0.54212	3.20490	-13.8522	<0.01	93.82	1.7e-4	834.07	<2.2e-16
0.00051	-2.58332	9.94920	-6.1042	0.01	1063.2	<2.2e-16	845.06	<2.2e-16
0.00056	-2.60152	13.05188	-7.2052	0.01	550.31	<2.2e-16	395.07	<2.2e-16

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VaR Prediction Model Based on Time-varying Extremum Method and Its Application

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