A Research Based On POT-CAViaR Model of Extreme Risk Measure

Baoshuai Zhang; Jun Duan

Open Access

A Research Based On POT-CAViaR Model of Extreme Risk Measure

Baoshuai Zhang

and

Jun Duan

| Aug 20, 2020

Applied Mathematics and Nonlinear Sciences

Volume 5 (2020): Issue 2 (July 2020)

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Page range: 461 - 472

Received: Nov 25, 2019

Accepted: Feb 01, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00040

Keywords
CAViaR Model, POT Model, Extreme Risk

© 2020 Baoshuai Zhang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Sequence diagram of the rate of return of the sample

POT model diagnosis diagram of HS300 extreme residual sequence

Extreme quantile 1% VaR posteriori test results

		Out-Sample(n = 500)

		POT-SAV	POT-AS	POT-IGARCH	GARCH-POT	POT
HS300	Failure N	9	8	7	9	10
	LR Statistics	2.61	1.54	0.72	2.61	3.91
	P	0.106	0.2149	0.3966	0.106	0.0479
HSI	Failure N	7	8	4	8	9
	LR Statistics	0.72	1.54	0.22	1.54	2.61
	P	0.3966	0.2149	0.6414	0.2149	0.106
N225	Failure N	6	7	3	8	9
	LR Statistics	0.19	0.72	0.94	1.54	2.61
	P	0.6630	0.3966	0.3314	0.2149	0.106

Quantile parameter estimation results of CAViaR class model

			β₁	β₂	β₃	β₄
SAV	HS300	1%	0.0729^**(0.0338)	0.9440^*(0.0381)	0.2393^*(0.0905)	-
	HS300	5%	0.0155^*£0.0033¤	0.9774^*£0.0087¤	0.0614^*£0.0155¤	-
	HSI	1%	0.1393^**(0.0667)	0.8291^*(0.0629)	0.3124^**£0.1374¤	-
	HSI	5%	0.0659^*£0.0659¤	0.9124^*£0.0251¤	0.1840^*£0.0218¤	-
	N225	1%	0.1833^*(0.0215)	0.8612^*(0.0128)	0.2871^*£0.0159¤	-
	N225	5%	0.0722^*£0.0072¤	0.9103^*£0.0115¤	0.1899^*£0.0222¤	-
AS	HS300	1%	0.0115^***£0.0585¤	0.9464^*£0.0791¤	0.209£0.2476¤	0.1537^***£0.1513¤
	HS300	5%	0.0011^***£0.0029¤	0.9782^*£0.0083¤	0.0472^***£0.0172¤	0.0514^*£0.0195¤
	HSI	1%	0.0916^***£0.0582¤	0.8513^*£0.0665¤	0.1649£0.1547¤	0.4753^*£0.1078¤
	HSI	5%	0.0271^*£0.0104¤	0.9067^*£0.0252¤	0.0550^***£0.0323¤	0.2449^*£0.0722¤
	N225	1%	0.1109^**£0.0385¤	0.8012^*£0.0922¤	0.2555£0.2640¤	0.6211^***£0.3828¤
	N225	5%	0.0314^*£0.0070¤	0.8939^*£0.0152¤	0.0466^***£0.0314¤	0.2814^*£0.0391¤
IGARCH	HS300	1%	0.0026^***£0.0294¤	0.9309^*£0.0150¤	0.5488£1.7734¤	-
	HS300	5%	0.0033^***£0.0030¤	0.9811^*£0.0031¤	0.0583£0.6437¤	-
	HSI	1%	0.1635^***£0.1237¤	0.7802^*£0.0653¤	1.1863£0.4317¤	-
	HSI	5%	0.0128^***£0.0089¤	0.9207^*£0.0141¤	0.1795^**£0.9726¤	-
	N225	1%	0.2110^*£0.0616¤	0.7647^*£0.0133¤	1.0777£0.9034¤	-
	N225	5%	0.0196^**£0.0094¤	0.9120^*£0.0052¤	0.1970^***£0.3962¤	-

The result of the posterior test based on the CAViaR class model

Out-Sample (n = 500)

		SAV		AS		IGARCH

		1%	5%	1%	5%	1%	5%
HS300	Failure N	15	29	19	31	14	30
	LR Statistics	13.16	0.64	23.13	1.41	10.99	0.3192
	P	0.0001	0.4229	0.0000	0.2346	0.0009	0.4229
HSI	Failure N	16	26	17	28	15	26
	LR Statistics	15.48	0.0416	17.90	0.37	13.16	0.0416
	P	0.0000	0.8384	0.0002	0.5455	0.0003	0.8384
N225	Failure N	16	26	18	28	13	27
	LR Statistics	15.48	0.0416	20.46	0.37	8.97	0.16
	P	0.0000	0.8384	0.0000	0.5455	0.0027	0.6852

Descriptive statistics of samples

Sample	Mean	Max	Min	SD	Skewness	Kurtosis	J-B
HS300	0.0200	3.8786	−4.4987	0.8460	−0.4424	6.4561	1419^*
HSI	0.0093	5.8225	−8.3011	0.7212	−0.3047	18.5013	26833^*
N225	0.0081	5.7478	−11.1353	0.7359	−1.6032	27.9836	70742^*

POT estimation of the extreme standard residual sequence

		SAV	AS	IGARCH
HS300	μ	0.916	0.851	0.926
	ξ	0.342	0.222	0.276
	σ	0.333	0.450	0.441
HSI	μ	0.731	0.704	0.671
	ξ	0.180	0.231	0.172
	σ	0.473	0.451	0.341
N225	μ	0.767	0.712	0.681
	ξ	0.172	0.213	0.351
	σ	0.365	0.461	0.672

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A Research Based On POT-CAViaR Model of Extreme Risk Measure

Published Online: Aug 20, 2020

Page range: 461 - 472

Received: Nov 25, 2019

Accepted: Feb 01, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00040

Keywords
CAViaR Model, POT Model, Extreme Risk

© 2020 Baoshuai Zhang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Extreme quantile 1% VaR posteriori test results

Quantile parameter estimation results of CAViaR class model

The result of the posterior test based on the CAViaR class model

Descriptive statistics of samples

POT estimation of the extreme standard residual sequence

A Research Based On POT-CAViaR Model of Extreme Risk Measure

Published Online: Aug 20, 2020

Page range: 461 - 472

Received: Nov 25, 2019

Accepted: Feb 01, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00040

KeywordsCAViaR Model, POT Model, Extreme Risk

© 2020 Baoshuai Zhang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Extreme quantile 1% VaR posteriori test results

Quantile parameter estimation results of CAViaR class model

The result of the posterior test based on the CAViaR class model

Descriptive statistics of samples

POT estimation of the extreme standard residual sequence

Keywords
CAViaR Model, POT Model, Extreme Risk