Table 7 In-sample pricing errors of SVI...

Table 7

In-sample pricing errors of SVI and 5th-order spline models for CSI 300 index options from January 4, 2021 to December 31, 2021

Model	Short (10–90 days)				Long (>90 days)
Model	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	20.77	32.87	2.65	694	25.63	28.12	12.82	879
Spline	5.82	11.09	1.28	743	16.24	16.71	12.13	1,203
B. OTM put (0.85<Moneyness<1)
SVI	3.86	15.18	12.21	6,885	−2.03	14.48	28.86	1,860
Spline	4.80	9.68	7.43	7,442	4.65	12.52	27.09	4,795
C. OTM call (1<Moneyness<1.15)
SVI	2.79	13.97	9.15	4,310	−3.43	14.65	27.36	1,084
Spline	−1.22	10.67	9.50	4,634	2.82	17.21	36.22	2,884
D. Deep OTM call (Moneyness>1.15)
SVI	−15.04	22.75	1.59	791	−15.92	18.90	9.23	460
Spline	−6.32	14.27	1.83	837	−17.04	22.99	14.44	1,162

Model	Short (10–90 days)				Long (>90 days)
Model	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	20.77	32.87	2.65	694	25.63	28.12	12.82	879
Spline	5.82	11.09	1.28	743	16.24	16.71	12.13	1,203
B. OTM put (0.85<Moneyness<1)
SVI	3.86	15.18	12.21	6,885	−2.03	14.48	28.86	1,860
Spline	4.80	9.68	7.43	7,442	4.65	12.52	27.09	4,795
C. OTM call (1<Moneyness<1.15)
SVI	2.79	13.97	9.15	4,310	−3.43	14.65	27.36	1,084
Spline	−1.22	10.67	9.50	4,634	2.82	17.21	36.22	2,884
D. Deep OTM call (Moneyness>1.15)
SVI	−15.04	22.75	1.59	791	−15.92	18.90	9.23	460
Spline	−6.32	14.27	1.83	837	−17.04	22.99	14.44	1,162

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. 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 (modified for known cash dividends) with the volatility from the SVI or spline model. N: number of options priced by the SVI or spline model

Source(s): Authors’ own work

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