Comparison of Block Maxima and Peaks Over Threshold Value-at-Risk models for market risk in various economic conditions

	VaR 99%	EX	Kupiec	Christoff	T_BP	A&B	Caporin	CAE
Emerging countries
Bulgaria (SOFIX)
BM_21,I	12.91	0	4.99 (0.03)	4.99 (0.08)	−1.58 (0.11)	<0.001	0.182	0.074
BM_42,I	13.87	0	4.99 (0.03)	4.99 (0.08)	−1.58 (0.11)	<0.001	0.196	0.079
POT_I	3.67	1	1.15 (0.28)	1.16 (0.56)	−0.95 (0.34)	<0.001	0.049	0.021
Czech R (PX)
BM_21,I	6.62	0	5.01 (0.03)	5.01 (0.08)	−1.59 (0.11)	<0.001	0.094	0.035
BM_42,I	7.19	0	5.01 (0.03)	5.01 (0.08)	−1.59 (0.11)	<0.001	0.103	0.038
POT_I	3.44	2	0.1 (0.75)	0.14 (0.93)	−0.31 (0.76)	<0.001	0.047	0.018
Lithuania (OMXV)
BM_21,I	5.49	0	4.84 (0.03)	4.84 (0.09)	−1.56 (0.12)	<0.001	0.076	0.031
BM_42,I	7.68	0	4.84 (0.03)	4.84 (0.09)	−1.56 (0.12)	<0.001	0.108	0.043
POT_I	2.20	9	10.72 (0)	11.67 (0)	4.27 (0)	<0.001	0.029	0.013
Latvia (OMXR)
BM_21,I	11.49	0	4.99 (0.03)	4.99 (0.08)	−1.58 (0.11)	<0.001	0.17	0.056
BM_42,I	15.78	0	4.99 (0.03)	4.99 (0.08)	−1.58 (0.11)	<0.001	0.235	0.076
POT_I	4.21	0	4.99 (0.03)	4.99 (0.08)	−1.58 (0.11)	<0.001	0.057	0.02
Poland (WIG20)
BM_21,I	6.95	0	4.99 (0.03)	4.99 (0.08)	−1.58 (0.11)	<0.001	0.099	0.035
BM_42,I	7.47	0	4.99 (0.03)	4.99 (0.08)	−1.58 (0.11)	<0.001	0.107	0.038
POT_I	4.00	2	0.1 (0.75)	0.13 (0.94)	−0.31 (0.76)	<0.001	0.054	0.02
Slovakia (SAX)
BM_21,I	7.63	0	4.86 (0.03)	4.86 (0.09)	−1.56 (0.12)	<0.001	0.097	0.054
BM_42,I	7.96	0	4.86 (0.03)	4.86 (0.09)	−1.56 (0.12)	<0.001	0.101	0.056
POT_I	3.52	0	4.86 (0.03)	4.86 (0.09)	−1.56 (0.12)	<0.001	0.043	0.024
Hungary (BUX)
BM_21,I	7.43	0	4.91 (0.03)	4.91 (0.09)	−1.57 (0.12)	<0.001	0.104	0.04
BM_42,I	8.67	0	4.91 (0.03)	4.91 (0.09)	−1.57 (0.12)	<0.001	0.122	0.047
POT_I	3.64	2	0.09 (0.77)	0.12 (0.94)	−0.28 (0.78)	<0.001	0.048	0.02
Developed countries
England (UKX)
BM_21,I	6.84	0	5.07 (0.02)	5.07(0.08)	−1.6 (0.11)	<0.001	0.095	0.037
BM_42,I	8.98	0	5.07 (0.02)	5.07 (0.08)	−1.6 (0.11)	<0.001	0.127	0.049
POT_I	3.25	3	0.09 (0.77)	0.16 (0.92)	0.3 (0.76)	<0.001	0.043	0.018
France (CAC)
BM_21,I	7.52	0	5.11 (0.02)	5.11 (0.08)	−1.6 (0.11)	<0.001	0.108	0.039
BM_42,I	8.70	0	5.11 (0.02)	5.11 (0.08)	−1.6 (0.11)	<0.001	0.125	0.045
POT_I	4.05	0	5.11 (0.02)	5.11 (0.08)	−1.6 (0.11)	<0.001	0.055	0.021
Germany (DAX)
BM_21,I	8.76	0	5.05 (0.02)	5.05 (0.08)	−1.59 (0.11)	<0.001	0.123	0.049
BM_42,I	9.70	0	5.05 (0.02)	5.05 (0.08)	−1.59 (0.11)	<0.001	0.137	0.054
POT_I	4.55	0	5.05 (0.02)	5.05 (0.08)	−1.59 (0.11)	<0.001	0.062	0.025

VaR forecasts for individual countries in period II

	VaR 99%	EX	Kupiec	Christoff	T_BP	A&B	Caporin	CAE
Emerging countries
Bulgaria (SOFIX)
BM_21,II	11.15	1	1.12 (0.29)	1.13 (0.57)	−0.93 (0.35)	<0.001	0.164	0.042
BM_42,II	11.24	1	1.12 (0.29)	1.13 (0.57)	−0.93 (0.35)	<0.001	0.165	0.042
POT_II	3.55	26	78.09 (0)	94.62 (0)	15.12 (0)	0.002	0.048	0.02
Czech R (PX)
BM_21,II	7.05	6	3.53 (0.06)	5.96 (0.05)	2.21 (0.03)	0.001	0.097	0.035
BM_42,II	7.56	5	1.94 (0.16)	2.14 (0.34)	1.58 (0.11)	0.001	0.105	0.037
POT_II	3.4	22	58.1 (0)	65.4 (0)	12.36 (0)	0.003	0.047	0.021
Lithuania (OMXV)
BM_21,II	5.87	4	0.87 (0.35)	12.96 (0)	1.02 (0.31)	<0.001	0.083	0.024
BM_42,II	7.86	3	0.13 (0.72)	15.65 (0)	0.38 (0.71)	<0.001	0.115	0.031
POT_II	2.33	25	73.79 (0)	87.66 (0)	14.59 (0)	0.002	0.032	0.014
Latvia (OMXR)
BM_21,II	11.04	0	4.97 (0.03)	4.97 (0.08)	−1.58 (0.11)	<0.001	0.163	0.046
BM_42,II	14.94	0	4.97 (0.03)	4.97 (0.08)	−1.58 (0.11)	<0.001	0.224	0.063
POT_II	4.06	11	16.1 (0)	28.57 (0)	5.46 (0)	0.001	0.055	0.02
Poland (WIG20)
BM_21,II	7.15	2	0.11 (0.74)	0.14 (0.93)	−0.32 (0.75)	<0.001	0.096	0.035
BM_42,II	8	1	1.18 (0.28)	1.19 (0.55)	−0.95 (0.34)	<0.001	0.109	0.038
POT_II	3.94	16	33.15 (0)	34 (0)	8.58 (0)	0.001	0.05	0.022
Slovakia (SAX)
BM_21,II	7.42	0	4.93 (0.03)	4.93 (0.09)	−1.57 (0.12)	<0.001	0.093	0.052
BM_42,II	7.74	0	4.93 (0.03)	4.93 (0.09)	−1.57 (0.12)	<0.001	0.097	0.054
POT_II	3.41	3	0.12 (0.73)	0.19 (0.91)	0.35 (0.72)	<0.001	0.04	0.024
Hungary (BUX)
BM_21,II	7.27	6	3.56 (0.06)	11.69 (0)	2.23 (0.03)	0.001	0.102	0.034
BM_42,II	8.32	4	0.77 (0.38)	4.88 (0.09)	0.95 (0.34)	<0.001	0.118	0.038
POT_II	3.57	14	25.78 (0)	27.32 (0)	7.31 (0)	0.002	0.048	0.02
Developed countries
England (UKX)
BM_21,II	6.99	3	0.08 (0.77)	0.16 (0.92)	0.3 (0.77)	<0.001	0.099	0.032
BM_42,II	8.91	1	1.21 (0.27)	1.22 (0.54)	−0.97 (0.33)	<0.001	0.129	0.039
POT_II	3.25	16	32.82 (0)	33.7 (0)	8.51 (0)	0.001	0.045	0.018
France (CAC)
BM_21,II	7.28	2	0.13 (0.72)	0.16 (0.92)	−0.35 (0.73)	<0.001	0.1	0.035
BM_42,II	8.65	1	1.24 (0.27)	1.25 (0.54)	−0.98 (0.33)	<0.001	0.121	0.041
POT_II	3.93	16	32.6 (0)	32.6 (0)	8.47 (0)	0.001	0.052	0.022
Germany (DAX)
BM_21,II	8.52	0	5.09 (0.02)	5.09 (0.08)	−1.6 (0.11)	<0.001	0.12	0.04
BM_42,II	9.74	0	5.09 (0.02)	5.09 (0.08)	−1.6 (0.11)	<0.001	0.138	0.045
POT_II	4.41	13	22.06 (0)	22.22 (0)	6.62 (0)	0.001	0.059	0.024

VaR forecasts for individual countries in period III

	VaR 99%	EX	Kupiec	Christoff	T_BP	A&B	Caporin	CAE
Emerging countries
Bulgaria (SOFIX)
BM_21,III	12.31	0	5.01 (0.03)	5.01 (0.08)	−1.59 (0.11)	<0.001	0.179	0.064
BM_42,III	11.9	0	5.01 (0.03)	5.01 (0.08)	−1.59 (0.11)	<0.001	0.173	0.062
POT_III	4.92	0	5.01 (0.03)	5.01 (0.08)	−1.59 (0.11)	<0.001	0.068	0.025
Czech R (PX)
BM_21,III	10.2	0	5.05 (0.02)	5.05 (0.08)	−1.59 (0.11)	<0.001	0.145	0.055
BM_42,III	11.88	0	5.05 (0.02)	5.05 (0.08)	−1.59 (0.11)	<0.001	0.169	0.064
POT_III	4.45	2	0.11 (0.74)	0.15 (0.93)	−0.32 (0.75)	<0.001	0.061	0.024
Lithuania (OMXV)
BM_21,III	7.72	0	4.93 (0.03)	4.93 (0.09)	−1.57 (0.12)	<0.001	0.11	0.044
BM_42,III	10.02	0	4.93 (0.03)	4.93 (0.09)	−1.57 (0.12)	<0.001	0.142	0.057
POT_III	3.2	1	1.12 (0.29)	1.13 (0.57)	−0.93 (0.35)	<0.001	0.046	0.019
Latvia (OMXR)
BM_21,III	13.06	0	4.97 (0.03)	4.97 (0.08)	−1.58 (0.11)	<0.001	0.192	0.065
BM_42,III	16.25	0	4.97 (0.03)	4.97 (0.08)	−1.58 (0.11)	<0.001	0.24	0.081
POT_III	4.85	0	4.97 (0.03)	4.97 (0.08)	−1.58 (0.11)	<0.001	0.07	0.024
Poland (WIG20)
BM_21,III	8.45	0	5.07 (0.02)	5.07 (0.08)	−1.6 (0.11)	<0.001	0.121	0.044
BM_42,III	9.46	0	5.07 (0.02)	5.07 (0.08)	−1.6 (0.11)	<0.001	0.136	0.049
POT_III	4.6	0	5.07 (0.02)	5.07 (0.08)	−1.6 (0.11)	<0.001	0.064	0.024
Slovakia (SAX)
BM_21,III	10.1	1	1.16 (0.28)	1.17 (0.56)	−0.95 (0.34)	<0.001	0.133	0.065
BM_42,III	11.41	1	1.16 (0.28)	1.17 (0.56)	−0.95 (0.34)	<0.001	0.151	0.073
POT_III	3.72	4	0.78(0.38)	0.91(0.63)	0.96 (0.34)	0.001	0.048	0.025
Hungary (BUX)
BM_21,III	9.64	0	5.09 (0.02)	5.09 (0.08)	−1.6 (0.11)	<0.001	0.139	0.048
BM_42,III	11.36	0	5.09 (0.02)	5.09 (0.08)	−1.6 (0.11)	<0.001	0.165	0.057
POT_III	4.48	4	0.73 (0.39)	0.86 (0.65)	0.93 (0.35)	<0.001	0.062	0.023
Developed countries
England (UKX)
BM_21,III	8.73	0	5.07 (0.02)	5.07 (0.08)	−1.6 (0.11)	<0.001	0.125	0.046
BM_42,III	10.61	0	5.07 (0.02)	5.07 (0.08)	−1.6 (0.11)	<0.001	0.153	0.056
POT_III	3.9	0	5.07 (0.02)	5.07 (0.08)	−1.6 (0.11)	<0.001	0.054	0.02
France (CAC)
BM_21,III	8.51	0	5.17 (0.02)	5.17 (0.08)	−1.61 (0.11)	<0.001	0.123	0.042
BM_42,III	9.69	0	5.17 (0.02)	5.17 (0.08)	−1.61 (0.11)	<0.001	0.141	0.048
POT_III	4.49	2	0.14 (0.71)	0.17 (0.92)	−0.36 (0.72)	<0.001	0.062	0.023
Germany (DAX)
BM_21,III	9.3	0	5.13 (0.02)	5.13 (0.08)	−1.61 (0.11)	<0.001	0.132	0.051
BM_42,III	10.25	0	5.13 (0.02)	5.13 (0.08)	−1.61 (0.11)	<0.001	0.145	0.056
POT_III	4.79	0	5.13 (0.02)	5.13 (0.08)	−1.61 (0.11)	<0.001	0.066	0.026

Descriptive statistics of time series of return rates from stock exchange indices from 2000 to 2009

Country	Avg	Min	SD	1P	Q1	Med	Q3	99P	Max	Sk	Kurt	JB	Cap
Emerging countries
Bulgaria	0.08	−11.36	1.59	−5.03	−0.52	0.08	0.69	4.99	8.39	−0.50	6.78	0.00	7
Czech R	0.03	−16.18	1.59	−4.21	−0.73	0.07	0.84	3.70	12.36	−0.49	12.07	0.00	37
Lithuania	0.03	−10.22	1.07	−3.33	−0.32	0.00	0.42	2.87	11.00	−0.18	18.93	0.00	4
Latvia	0.04	−14.70	1.62	−4.82	−0.51	0.02	0.61	4.75	10.18	−0.73	14.83	0.00	1
Poland	0.01	−8.44	1.73	−4.47	−0.96	0.00	0.94	4.56	8.15	−0.09	1.81	0.00	178
Slovakia	0.05	−9.58	1.23	−3.69	−0.34	0.00	0.46	3.85	11.88	−0.16	10.73	0.00	5
Hungary	0.04	−12.65	1.68	−4.17	−0.88	0.05	0.94	4.42	13.18	−0.13	5.82	0.00	21
Developed countries
England	−0.01	−9.27	1.34	−4.02	−0.64	0.03	0.66	3.50	9.38	−0.12	6.11	0.00	3 019
France	−0.02	−9.47	1.58	−4.43	−0.77	0.02	0.78	4.07	10.60	0.03	4.95	0.00	1 823
Germany	0.00	−8.88	1.68	−5.04	−0.84	0.07	0.85	4.68	10.80	0.04	4.21	0.00	1 486

eISSN:: 2543-6821
Language:: English

Publication timeframe:: Volume Open
Journal Subjects:: Business and Economics, Political Economics, Economic Theory, Systems and Structures, Microeconomics, Macroecomics, Economic Policy

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Comparison of Block Maxima and Peaks Over Threshold Value-at-Risk models for market risk in various economic conditions

Published Online: Mar 13, 2020

Page range: 70 - 85

DOI: https://doi.org/10.2478/ceej-2019-0005

KeywordsValue-at-Risk, extreme value theory, forecasting, market risk

© 2019 Filip Szubzda et al., published by Sciendo

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

VaR forecasts for individual countries in period I

VaR forecasts for individual countries in period II

VaR forecasts for individual countries in period III

Descriptive statistics of time series of return rates from stock exchange indices from 2000 to 2009

Keywords
Value-at-Risk, extreme value theory, forecasting, market risk