Table 9 In-sample pricing errors of SVI...

Table 9

In-sample pricing errors of SVI and 5th-order spline models for copper futures options from November 2, 2020 to October 29, 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	25.5	44.49	35.39	811	8.83	21.76	68.36	1,363
Spline	−0.29	10.77	5.49	1,865	0.17	3.81	6.24	1,565
B. OTM put (0.85<Moneyness<1)
SVI	27.61	28.70	77.72	2,806	9.77	11.76	117.41	695
Spline	1.75	5.34	25.60	3,477	0.19	1.99	40.58	774
C. OTM call (1<Moneyness<1.15)
SVI	6.65	8.23	46.31	2,451	5.41	6.44	141.38	635
Spline	−0.38	3.83	32.74	2,763	0.14	1.21	54.63	683
D. Deep OTM call (Moneyness>1.15)
SVI	−0.13	17.20	17.49	220	4.84	8.02	93.72	53
Spline	0.24	6.50	4.90	261	−0.09	1.23	6.24	45

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	25.5	44.49	35.39	811	8.83	21.76	68.36	1,363
Spline	−0.29	10.77	5.49	1,865	0.17	3.81	6.24	1,565
B. OTM put (0.85<Moneyness<1)
SVI	27.61	28.70	77.72	2,806	9.77	11.76	117.41	695
Spline	1.75	5.34	25.60	3,477	0.19	1.99	40.58	774
C. OTM call (1<Moneyness<1.15)
SVI	6.65	8.23	46.31	2,451	5.41	6.44	141.38	635
Spline	−0.38	3.83	32.74	2,763	0.14	1.21	54.63	683
D. Deep OTM call (Moneyness>1.15)
SVI	−0.13	17.20	17.49	220	4.84	8.02	93.72	53
Spline	0.24	6.50	4.90	261	−0.09	1.23	6.24	45

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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