Table 4 Open in new tab Implied moment...

Panel A. Implied volatility estimates
Mean	0.161	0.160	0.159	0.157	0.147	0.000	0.000	0.000	0.000	0.000
Std. dev.	0.102	0.101	0.101	0.101	0.096	0.039	0.040	0.039	0.039	0.037
5th pct.	0.076	0.075	0.074	0.073	0.066	−0.047	−0.047	−0.047	−0.045	−0.042
25th pct.	0.103	0.102	0.101	0.100	0.092	−0.014	−0.014	−0.013	−0.013	−0.012
Median	0.135	0.135	0.133	0.132	0.123	0.000	−0.001	−0.001	−0.001	−0.001
75th pct.	0.187	0.185	0.184	0.182	0.170	0.011	0.010	0.010	0.010	0.009
95th pct.	0.317	0.313	0.312	0.308	0.288	0.048	0.046	0.045	0.044	0.042
Skewness	4.048	4.068	4.094	4.125	4.208	2.432	2.425	2.402	2.354	2.256
Kurtosis	29.024	29.266	29.617	30.072	31.268	35.382	37.092	37.824	37.854	38.232
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Panel A. Implied volatility estimates

Level

First-order difference

Intensity

25%

50%

75%

100%

25%

50%

75%

100%

Mean

0.161

0.160

0.159

0.157

0.147

0.000

Std. dev.

0.102

0.101

0.096

0.039

0.040

0.039

0.037

5th pct.

0.076

0.075

0.074

0.073

0.066

−0.047

−0.045

−0.042

25th pct.

0.103

0.102

0.101

0.100

0.092

−0.014

−0.013

−0.012

Median

0.135

0.133

0.132

0.123

0.000

−0.001

75th pct.

0.187

0.185

0.184

0.182

0.170

0.011

0.010

0.009

95th pct.

0.317

0.313

0.312

0.308

0.288

0.048

0.046

0.045

0.044

0.042

Skewness

4.048

4.068

4.094

4.125

4.208

2.432

2.425

2.402

2.354

2.256

Kurtosis

29.024

29.266

29.617

30.072

31.268

35.382

37.092

37.824

37.854

38.232

# of obs.

1,528

1,527

Panel A. Implied volatility estimates
Mean	0.161	0.160	0.159	0.157	0.147	0.000	0.000	0.000	0.000	0.000
Std. dev.	0.102	0.101	0.101	0.101	0.096	0.039	0.040	0.039	0.039	0.037
5th pct.	0.076	0.075	0.074	0.073	0.066	−0.047	−0.047	−0.047	−0.045	−0.042
25th pct.	0.103	0.102	0.101	0.100	0.092	−0.014	−0.014	−0.013	−0.013	−0.012
Median	0.135	0.135	0.133	0.132	0.123	0.000	−0.001	−0.001	−0.001	−0.001
75th pct.	0.187	0.185	0.184	0.182	0.170	0.011	0.010	0.010	0.010	0.009
95th pct.	0.317	0.313	0.312	0.308	0.288	0.048	0.046	0.045	0.044	0.042
Skewness	4.048	4.068	4.094	4.125	4.208	2.432	2.425	2.402	2.354	2.256
Kurtosis	29.024	29.266	29.617	30.072	31.268	35.382	37.092	37.824	37.854	38.232
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Panel B. Implied skewness estimates
Mean	−2.127	−1.992	−1.839	−1.658	−1.292	0.000	0.000	0.000	0.000	0.000
Std. dev.	0.954	0.722	0.562	0.430	0.198	0.542	0.391	0.309	0.246	0.124
5th pct.	−4.020	−3.342	−2.862	−2.425	−1.633	−0.878	−0.638	−0.493	−0.392	−0.201
25th pct.	−2.633	−2.455	−2.198	−1.921	−1.415	−0.282	−0.232	−0.182	−0.145	−0.072
Median	−1.902	−1.895	−1.781	−1.617	−1.277	0.010	0.000	−0.004	−0.005	−0.001
75th pct.	−1.393	−1.414	−1.406	−1.335	−1.150	0.270	0.225	0.180	0.147	0.076
95th pct.	−1.000	−1.041	−1.057	−1.043	−1.004	0.901	0.656	0.510	0.394	0.199
Skewness	−1.094	−0.737	−0.661	−0.676	−0.638	−0.215	−0.140	−0.082	−0.035	−0.055
Kurtosis	4.101	3.295	3.380	3.659	3.860	6.669	4.765	4.592	4.882	5.392
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Panel B. Implied skewness estimates

Level

First-order difference

Intensity

25%

50%

75%

100%

25%

50%

75%

100%

Mean

−2.127

−1.992

−1.839

−1.658

−1.292

0.000

Std. dev.

0.954

0.722

0.562

0.430

0.198

0.542

0.391

0.309

0.246

0.124

5th pct.

−4.020

−3.342

−2.862

−2.425

−1.633

−0.878

−0.638

−0.493

−0.392

−0.201

25th pct.

−2.633

−2.455

−2.198

−1.921

−1.415

−0.282

−0.232

−0.182

−0.145

−0.072

Median

−1.902

−1.895

−1.781

−1.617

−1.277

0.010

0.000

−0.004

−0.005

−0.001

75th pct.

−1.393

−1.414

−1.406

−1.335

−1.150

0.270

0.225

0.180

0.147

0.076

95th pct.

−1.000

−1.041

−1.057

−1.043

−1.004

0.901

0.656

0.510

0.394

0.199

Skewness

−1.094

−0.737

−0.661

−0.676

−0.638

−0.215

−0.140

−0.082

−0.035

−0.055

Kurtosis

4.101

3.295

3.380

3.659

3.860

6.669

4.765

4.592

4.882

5.392

# of obs.

1,528

1,527

Panel B. Implied skewness estimates
Mean	−2.127	−1.992	−1.839	−1.658	−1.292	0.000	0.000	0.000	0.000	0.000
Std. dev.	0.954	0.722	0.562	0.430	0.198	0.542	0.391	0.309	0.246	0.124
5th pct.	−4.020	−3.342	−2.862	−2.425	−1.633	−0.878	−0.638	−0.493	−0.392	−0.201
25th pct.	−2.633	−2.455	−2.198	−1.921	−1.415	−0.282	−0.232	−0.182	−0.145	−0.072
Median	−1.902	−1.895	−1.781	−1.617	−1.277	0.010	0.000	−0.004	−0.005	−0.001
75th pct.	−1.393	−1.414	−1.406	−1.335	−1.150	0.270	0.225	0.180	0.147	0.076
95th pct.	−1.000	−1.041	−1.057	−1.043	−1.004	0.901	0.656	0.510	0.394	0.199
Skewness	−1.094	−0.737	−0.661	−0.676	−0.638	−0.215	−0.140	−0.082	−0.035	−0.055
Kurtosis	4.101	3.295	3.380	3.659	3.860	6.669	4.765	4.592	4.882	5.392
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Panel C. Implied kurtosis estimates
Mean	14.828	12.206	10.097	8.073	4.187	0.007	0.004	0.002	0.000	0.000
Std. dev.	9.966	5.846	3.793	2.382	0.711	6.026	3.119	1.976	1.271	0.394
5th pct.	5.161	5.114	5.072	4.846	3.233	−9.006	−5.255	−3.118	−2.043	−0.622
25th pct.	7.435	7.376	7.077	6.259	3.680	−2.165	−1.618	−1.130	−0.716	−0.218
Median	11.549	11.082	9.544	7.706	4.069	−0.128	−0.108	−0.046	−0.022	−0.004
75th pct.	18.920	15.658	12.434	9.466	4.607	2.153	1.577	1.120	0.735	0.221
95th pct.	36.234	23.355	17.017	12.447	5.514	9.039	5.165	3.175	1.949	0.593
Skewness	1.605	0.909	0.797	0.857	0.962	0.170	0.215	0.169	0.099	0.027
Kurtosis	5.792	3.523	3.552	4.004	4.520	10.639	5.829	5.627	6.235	6.889
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Panel C. Implied kurtosis estimates

Level

First-order difference

Intensity

25%

50%

75%

100%

25%

50%

75%

100%

Mean

14.828

12.206

10.097

8.073

4.187

0.007

0.004

0.002

0.000

Std. dev.

9.966

5.846

3.793

2.382

0.711

6.026

3.119

1.976

1.271

0.394

5th pct.

5.161

5.114

5.072

4.846

3.233

−9.006

−5.255

−3.118

−2.043

−0.622

25th pct.

7.435

7.376

7.077

6.259

3.680

−2.165

−1.618

−1.130

−0.716

−0.218

Median

11.549

11.082

9.544

7.706

4.069

−0.128

−0.108

−0.046

−0.022

−0.004

75th pct.

18.920

15.658

12.434

9.466

4.607

2.153

1.577

1.120

0.735

0.221

95th pct.

36.234

23.355

17.017

12.447

5.514

9.039

5.165

3.175

1.949

0.593

Skewness

1.605

0.909

0.797

0.857

0.962

0.170

0.215

0.169

0.099

0.027

Kurtosis

5.792

3.523

3.552

4.004

4.520

10.639

5.829

5.627

6.235

6.889

# of obs.

1,528

1,527

Panel C. Implied kurtosis estimates
Mean	14.828	12.206	10.097	8.073	4.187	0.007	0.004	0.002	0.000	0.000
Std. dev.	9.966	5.846	3.793	2.382	0.711	6.026	3.119	1.976	1.271	0.394
5th pct.	5.161	5.114	5.072	4.846	3.233	−9.006	−5.255	−3.118	−2.043	−0.622
25th pct.	7.435	7.376	7.077	6.259	3.680	−2.165	−1.618	−1.130	−0.716	−0.218
Median	11.549	11.082	9.544	7.706	4.069	−0.128	−0.108	−0.046	−0.022	−0.004
75th pct.	18.920	15.658	12.434	9.466	4.607	2.153	1.577	1.120	0.735	0.221
95th pct.	36.234	23.355	17.017	12.447	5.514	9.039	5.165	3.175	1.949	0.593
Skewness	1.605	0.909	0.797	0.857	0.962	0.170	0.215	0.169	0.099	0.027
Kurtosis	5.792	3.523	3.552	4.004	4.520	10.639	5.829	5.627	6.235	6.889
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Table 4

Open in new tab

Implied moment estimates after applying DStab

Panel A. Implied volatility estimates
	Level					First-order difference
Intensity	0%	25%	50%	75%	100%	0%	25%	50%	75%	100%
Mean	0.161	0.160	0.159	0.157	0.147	0.000	0.000	0.000	0.000	0.000
Std. dev.	0.102	0.101	0.101	0.101	0.096	0.039	0.040	0.039	0.039	0.037
5th pct.	0.076	0.075	0.074	0.073	0.066	−0.047	−0.047	−0.047	−0.045	−0.042
25th pct.	0.103	0.102	0.101	0.100	0.092	−0.014	−0.014	−0.013	−0.013	−0.012
Median	0.135	0.135	0.133	0.132	0.123	0.000	−0.001	−0.001	−0.001	−0.001
75th pct.	0.187	0.185	0.184	0.182	0.170	0.011	0.010	0.010	0.010	0.009
95th pct.	0.317	0.313	0.312	0.308	0.288	0.048	0.046	0.045	0.044	0.042
Skewness	4.048	4.068	4.094	4.125	4.208	2.432	2.425	2.402	2.354	2.256
Kurtosis	29.024	29.266	29.617	30.072	31.268	35.382	37.092	37.824	37.854	38.232
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Panel A. Implied volatility estimates
	Level					First-order difference
Intensity	0%	25%	50%	75%	100%	0%	25%	50%	75%	100%
Mean	0.161	0.160	0.159	0.157	0.147	0.000	0.000	0.000	0.000	0.000
Std. dev.	0.102	0.101	0.101	0.101	0.096	0.039	0.040	0.039	0.039	0.037
5th pct.	0.076	0.075	0.074	0.073	0.066	−0.047	−0.047	−0.047	−0.045	−0.042
25th pct.	0.103	0.102	0.101	0.100	0.092	−0.014	−0.014	−0.013	−0.013	−0.012
Median	0.135	0.135	0.133	0.132	0.123	0.000	−0.001	−0.001	−0.001	−0.001
75th pct.	0.187	0.185	0.184	0.182	0.170	0.011	0.010	0.010	0.010	0.009
95th pct.	0.317	0.313	0.312	0.308	0.288	0.048	0.046	0.045	0.044	0.042
Skewness	4.048	4.068	4.094	4.125	4.208	2.432	2.425	2.402	2.354	2.256
Kurtosis	29.024	29.266	29.617	30.072	31.268	35.382	37.092	37.824	37.854	38.232
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Panel B. Implied skewness estimates
	Level					First-order difference
Intensity	0%	25%	50%	75%	100%	0%	25%	50%	75%	100%
Mean	−2.127	−1.992	−1.839	−1.658	−1.292	0.000	0.000	0.000	0.000	0.000
Std. dev.	0.954	0.722	0.562	0.430	0.198	0.542	0.391	0.309	0.246	0.124
5th pct.	−4.020	−3.342	−2.862	−2.425	−1.633	−0.878	−0.638	−0.493	−0.392	−0.201
25th pct.	−2.633	−2.455	−2.198	−1.921	−1.415	−0.282	−0.232	−0.182	−0.145	−0.072
Median	−1.902	−1.895	−1.781	−1.617	−1.277	0.010	0.000	−0.004	−0.005	−0.001
75th pct.	−1.393	−1.414	−1.406	−1.335	−1.150	0.270	0.225	0.180	0.147	0.076
95th pct.	−1.000	−1.041	−1.057	−1.043	−1.004	0.901	0.656	0.510	0.394	0.199
Skewness	−1.094	−0.737	−0.661	−0.676	−0.638	−0.215	−0.140	−0.082	−0.035	−0.055
Kurtosis	4.101	3.295	3.380	3.659	3.860	6.669	4.765	4.592	4.882	5.392
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Panel B. Implied skewness estimates
	Level					First-order difference
Intensity	0%	25%	50%	75%	100%	0%	25%	50%	75%	100%
Mean	−2.127	−1.992	−1.839	−1.658	−1.292	0.000	0.000	0.000	0.000	0.000
Std. dev.	0.954	0.722	0.562	0.430	0.198	0.542	0.391	0.309	0.246	0.124
5th pct.	−4.020	−3.342	−2.862	−2.425	−1.633	−0.878	−0.638	−0.493	−0.392	−0.201
25th pct.	−2.633	−2.455	−2.198	−1.921	−1.415	−0.282	−0.232	−0.182	−0.145	−0.072
Median	−1.902	−1.895	−1.781	−1.617	−1.277	0.010	0.000	−0.004	−0.005	−0.001
75th pct.	−1.393	−1.414	−1.406	−1.335	−1.150	0.270	0.225	0.180	0.147	0.076
95th pct.	−1.000	−1.041	−1.057	−1.043	−1.004	0.901	0.656	0.510	0.394	0.199
Skewness	−1.094	−0.737	−0.661	−0.676	−0.638	−0.215	−0.140	−0.082	−0.035	−0.055
Kurtosis	4.101	3.295	3.380	3.659	3.860	6.669	4.765	4.592	4.882	5.392
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Panel C. Implied kurtosis estimates
	Level					First-order difference
Intensity	0%	25%	50%	75%	100%	0%	25%	50%	75%	100%
Mean	14.828	12.206	10.097	8.073	4.187	0.007	0.004	0.002	0.000	0.000
Std. dev.	9.966	5.846	3.793	2.382	0.711	6.026	3.119	1.976	1.271	0.394
5th pct.	5.161	5.114	5.072	4.846	3.233	−9.006	−5.255	−3.118	−2.043	−0.622
25th pct.	7.435	7.376	7.077	6.259	3.680	−2.165	−1.618	−1.130	−0.716	−0.218
Median	11.549	11.082	9.544	7.706	4.069	−0.128	−0.108	−0.046	−0.022	−0.004
75th pct.	18.920	15.658	12.434	9.466	4.607	2.153	1.577	1.120	0.735	0.221
95th pct.	36.234	23.355	17.017	12.447	5.514	9.039	5.165	3.175	1.949	0.593
Skewness	1.605	0.909	0.797	0.857	0.962	0.170	0.215	0.169	0.099	0.027
Kurtosis	5.792	3.523	3.552	4.004	4.520	10.639	5.829	5.627	6.235	6.889
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Panel C. Implied kurtosis estimates
	Level					First-order difference
Intensity	0%	25%	50%	75%	100%	0%	25%	50%	75%	100%
Mean	14.828	12.206	10.097	8.073	4.187	0.007	0.004	0.002	0.000	0.000
Std. dev.	9.966	5.846	3.793	2.382	0.711	6.026	3.119	1.976	1.271	0.394
5th pct.	5.161	5.114	5.072	4.846	3.233	−9.006	−5.255	−3.118	−2.043	−0.622
25th pct.	7.435	7.376	7.077	6.259	3.680	−2.165	−1.618	−1.130	−0.716	−0.218
Median	11.549	11.082	9.544	7.706	4.069	−0.128	−0.108	−0.046	−0.022	−0.004
75th pct.	18.920	15.658	12.434	9.466	4.607	2.153	1.577	1.120	0.735	0.221
95th pct.	36.234	23.355	17.017	12.447	5.514	9.039	5.165	3.175	1.949	0.593
Skewness	1.605	0.909	0.797	0.857	0.962	0.170	0.215	0.169	0.099	0.027
Kurtosis	5.792	3.523	3.552	4.004	4.520	10.639	5.829	5.627	6.235	6.889
# of obs.	1,528	1,528	1,528	1,528	1,528	1,527	1,527	1,527	1,527	1,527

Notes: This table provides summary statistics for the levels and first-order differences of implied moment estimates after applying DStab at various intensity levels. Panels A, B, and C present the summary statistics for implied volatility, skewness, and kurtosis estimates, respectively. The table reports statistics for intensity levels of 0%, 25%, 50%, 75%, and 100%.

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