Table 11 Out-of-sample pricing errors of...

Table 11

Out-of-sample pricing errors of China 50 ETF options from January 4, 2021 to December 31, 2021

	Short (10–90 days)				Long (>90 days)
	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	−2.73	22.37	0.0012	181	8.66	12.24	0.0036	135
Spline	−12.21	19.94	0.0010	181	−2.75	8.23	0.0023	140
Linear	−10.94	19.24	0.0009	181	−1.65	8.03	0.0023	140
iCubic	−7.49	16.68	0.0008	181	−1.08	7.66	0.0023	140
B. OTM put (0.85<Moneyness<1)
SVI	12.50	18.77	0.0051	2091	−1.86	10.18	0.0142	714
Spline	−1.56	11.45	0.0039	2,115	−1.33	6.97	0.0105	839
Linear	−0.90	10.48	0.0032	2,115	−0.15	4.72	0.0073	839
iCubic	−0.67	10.32	0.0032	2,115	−0.12	4.69	0.0075	839
C. OTM call (1<Moneyness<1.15)
SVI	18.65	22.45	0.0059	2063	3.33	7.94	0.0109	685
Spline	0.59	12.10	0.0043	2087	2.75	7.34	0.0120	819
Linear	−0.01	11.06	0.0040	2087	1.08	4.78	0.0085	819
iCubic	0.04	10.83	0.0040	2087	0.99	4.74	0.0086	819
D. Deep OTM call (Moneyness>1.15)
SVI	3.05	25.20	0.0013	622	−0.74	8.87	0.0031	273
Spline	−10.50	17.71	0.0009	623	−3.11	8.24	0.0033	365
Linear	−7.48	15.46	0.0008	623	−0.52	6.18	0.0025	365
iCubic	−5.11	13.68	0.0007	623	0.27	5.88	0.0024	365

	Short (10–90 days)				Long (>90 days)
	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	−2.73	22.37	0.0012	181	8.66	12.24	0.0036	135
Spline	−12.21	19.94	0.0010	181	−2.75	8.23	0.0023	140
Linear	−10.94	19.24	0.0009	181	−1.65	8.03	0.0023	140
iCubic	−7.49	16.68	0.0008	181	−1.08	7.66	0.0023	140
B. OTM put (0.85<Moneyness<1)
SVI	12.50	18.77	0.0051	2091	−1.86	10.18	0.0142	714
Spline	−1.56	11.45	0.0039	2,115	−1.33	6.97	0.0105	839
Linear	−0.90	10.48	0.0032	2,115	−0.15	4.72	0.0073	839
iCubic	−0.67	10.32	0.0032	2,115	−0.12	4.69	0.0075	839
C. OTM call (1<Moneyness<1.15)
SVI	18.65	22.45	0.0059	2063	3.33	7.94	0.0109	685
Spline	0.59	12.10	0.0043	2087	2.75	7.34	0.0120	819
Linear	−0.01	11.06	0.0040	2087	1.08	4.78	0.0085	819
iCubic	0.04	10.83	0.0040	2087	0.99	4.74	0.0086	819
D. Deep OTM call (Moneyness>1.15)
SVI	3.05	25.20	0.0013	622	−0.74	8.87	0.0031	273
Spline	−10.50	17.71	0.0009	623	−3.11	8.24	0.0033	365
Linear	−7.48	15.46	0.0008	623	−0.52	6.18	0.0025	365
iCubic	−5.11	13.68	0.0007	623	0.27	5.88	0.0024	365

Note(s): OTM: out-of-the-money. SVI: the SSVI model of Gatheral and Jacquier (2014). Spline: 5th-order spline interpolation with one knot at moneyness one. Linear: linear interpolation on implied variance. iCubic: interpolating cubic spline on implied volatility. Short/Long: maturity in calendar days. MPE: $\frac{1}{n} \sum (P^{\mod} - P^{m k t}) / P^{m k t}$ ⁠. MAE: $\frac{1}{n} \sum | P^{\mod} - P^{m k t} | / P^{m k t}$ ⁠. RMSE: $\sqrt{\frac{1}{n} \sum {(P^{\mod} - P^{m k t})}^{2}}$ ⁠. $P^{m k t}$ ⁠: market option price. $P^{\mod}$ ⁠: Black-Scholes-Merton option price with a volatility forecasted from the previous trading day. N: number of out-of-sample options

Source(s): Authors’ own work

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