Table 5 Means and standard deviations of...

Table 5

Means and standard deviations of estimated SVI-JW parameters within the sample periods

Maturity		$v_{τ}$	$ψ_{τ}$	$p_{τ}$	$c_{τ}$	${\tilde{v}}_{τ}$	$N$	V (%)
A: China 50 ETF options
10–90 days	Mean	0.0367	−0.0015	0.4367	0.4337	0.0360	437	98.6
10–90 days	SD	0.0094	0.0506	0.1347	0.1426	0.0094
>90 days	Mean	0.0418	−0.0571	0.5322	0.4179	0.0400	139	84.8
>90 days	SD	0.0086	0.0757	0.2426	0.1520	0.0086
All	Mean	0.0379	−0.0149	0.4597	0.4299	0.0370	576	94.9
All	SD	0.0095	0.0624	0.1719	0.1450	0.0093
B: CSI 300 index options
10–90 days	Mean	0.0351	−0.0541	0.5419	0.4336	0.0338	587	92.4
10–90 days	SD	0.0127	0.0703	0.1962	0.1522	0.0126
>90 days	Mean	0.0337	−0.1429	0.7181	0.4322	0.0306	270	37.1
>90 days	SD	0.0099	0.0906	0.2331	0.1610	0.0101
All	Mean	0.0347	−0.0821	0.5974	0.4332	0.0327	857	62.9
All	SD	0.0119	0.0876	0.2239	0.1549	0.0120
C: Soybean meal futures options
10–90 days	Mean	0.0339	0.0885	0.4019	0.5788	0.0322	308	97.2
10–90 days	SD	0.0080	0.0641	0.1154	0.1736	0.0072
91–180 days	Mean	0.0328	0.0995	0.4090	0.6079	0.0310	277	97.9
91–180 days	SD	0.0071	0.0625	0.1103	0.1595	0.0068
>180 days	Mean	0.0297	0.1091	0.3581	0.5763	0.0277	162	97.0
>180 days	SD	0.0035	0.0604	0.1070	0.1720	0.0035
All	Mean	0.0326	0.0970	0.3950	0.5891	0.0308	747	97.4
All	SD	0.0071	0.0632	0.1133	0.1686	0.0066
D: Copper futures options
10–90 days	Mean	0.0400	0.0016	0.5981	0.6013	0.0393	332	89.2
10–90 days	SD	0.0094	0.0803	0.1914	0.2304	0.0091
>90 days	Mean	0.0403	0.0647	0.4079	0.5372	0.0385	209	93.3
>90 days	SD	0.0131	0.0979	0.1527	0.2712	0.0120
All	Mean	0.0410	0.0260	0.5246	0.5766	0.0390	541	90.8
All	SD	0.0110	0.0927	0.2000	0.2487	0.0103

Maturity		$v_{τ}$	$ψ_{τ}$	$p_{τ}$	$c_{τ}$	${\tilde{v}}_{τ}$	$N$	V (%)
A: China 50 ETF options
10–90 days	Mean	0.0367	−0.0015	0.4367	0.4337	0.0360	437	98.6
10–90 days	SD	0.0094	0.0506	0.1347	0.1426	0.0094
>90 days	Mean	0.0418	−0.0571	0.5322	0.4179	0.0400	139	84.8
>90 days	SD	0.0086	0.0757	0.2426	0.1520	0.0086
All	Mean	0.0379	−0.0149	0.4597	0.4299	0.0370	576	94.9
All	SD	0.0095	0.0624	0.1719	0.1450	0.0093
B: CSI 300 index options
10–90 days	Mean	0.0351	−0.0541	0.5419	0.4336	0.0338	587	92.4
10–90 days	SD	0.0127	0.0703	0.1962	0.1522	0.0126
>90 days	Mean	0.0337	−0.1429	0.7181	0.4322	0.0306	270	37.1
>90 days	SD	0.0099	0.0906	0.2331	0.1610	0.0101
All	Mean	0.0347	−0.0821	0.5974	0.4332	0.0327	857	62.9
All	SD	0.0119	0.0876	0.2239	0.1549	0.0120
C: Soybean meal futures options
10–90 days	Mean	0.0339	0.0885	0.4019	0.5788	0.0322	308	97.2
10–90 days	SD	0.0080	0.0641	0.1154	0.1736	0.0072
91–180 days	Mean	0.0328	0.0995	0.4090	0.6079	0.0310	277	97.9
91–180 days	SD	0.0071	0.0625	0.1103	0.1595	0.0068
>180 days	Mean	0.0297	0.1091	0.3581	0.5763	0.0277	162	97.0
>180 days	SD	0.0035	0.0604	0.1070	0.1720	0.0035
All	Mean	0.0326	0.0970	0.3950	0.5891	0.0308	747	97.4
All	SD	0.0071	0.0632	0.1133	0.1686	0.0066
D: Copper futures options
10–90 days	Mean	0.0400	0.0016	0.5981	0.6013	0.0393	332	89.2
10–90 days	SD	0.0094	0.0803	0.1914	0.2304	0.0091
>90 days	Mean	0.0403	0.0647	0.4079	0.5372	0.0385	209	93.3
>90 days	SD	0.0131	0.0979	0.1527	0.2712	0.0120
All	Mean	0.0410	0.0260	0.5246	0.5766	0.0390	541	90.8
All	SD	0.0110	0.0927	0.2000	0.2487	0.0103

Note(s): SVI-JW: SVI jump-wings parameters converted from the SSVI parameters (see Section 4.x for details). $v_{τ}$ ⁠: ATM variance, the squared implied ATM volatility. $ψ_{τ}$ ⁠: ATM skew. $p_{τ}$ ⁠: slope of the left/put wing. $c_{τ}$ ⁠: slope of the right/call wing. ${\tilde{v}}_{τ}$ ⁠: minimum implied variance. Maturity: in calendar days. Sample periods for options on China 50 ETF, CSI 300 index and soybean meal futures are between January 4, 2021 and December 31, 2021. Copper futures options data are between November 2, 2020 and October 29, 2021. SD: standard deviation. N: number of optimal SVI curves. V: N as a percentage of all possible trading-expiry days combinations within the samples

Source(s): Authors’ own work

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