Table 6 In-sample pricing errors of SVI...

Table 6

In-sample pricing errors of SVI and 5th-order spline models for 50ETF 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	−7.75	16.98	0.0008	182	7.13	8.14	0.0024	140
Spline	−0.68	3.29	0.0003	182	−1.79	3.59	0.0009	145
B. OTM put (0.85<Moneyness<1)
SVI	4.41	9.76	0.0038	2,139	−3.82	8.31	0.0139	746
Spline	−0.31	4.10	0.0028	2,171	−1.28	5.07	0.0094	863
C. OTM call (1<Moneyness<1.15)
SVI	9.88	12.18	0.0038	2,113	1.61	5.39	0.0081	712
Spline	1.45	3.93	0.0026	2,139	2.37	5.16	0.0103	843
D. Deep OTM call (Moneyness>1.15)
SVI	−3.31	20.46	0.0010	623	−2.23	5.81	0.0018	281
Spline	−1.48	7.50	0.0004	624	−1.04	6.39	0.0028	366

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	−7.75	16.98	0.0008	182	7.13	8.14	0.0024	140
Spline	−0.68	3.29	0.0003	182	−1.79	3.59	0.0009	145
B. OTM put (0.85<Moneyness<1)
SVI	4.41	9.76	0.0038	2,139	−3.82	8.31	0.0139	746
Spline	−0.31	4.10	0.0028	2,171	−1.28	5.07	0.0094	863
C. OTM call (1<Moneyness<1.15)
SVI	9.88	12.18	0.0038	2,113	1.61	5.39	0.0081	712
Spline	1.45	3.93	0.0026	2,139	2.37	5.16	0.0103	843
D. Deep OTM call (Moneyness>1.15)
SVI	−3.31	20.46	0.0010	623	−2.23	5.81	0.0018	281
Spline	−1.48	7.50	0.0004	624	−1.04	6.39	0.0028	366

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 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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