Table 8 In-sample pricing errors of SVI...

Table 8

In-sample pricing errors of SVI and 5th-order spline models for soybean meal futures options from January 4, 2021 to December 31, 2021

Model	Short (10–90 days)				Medium (91–180 days)				Long (>180 days)
Model	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	−6.92	13.17	1.06	234	−1.01	11.27	1.88	826	−0.07	4.88	1.80	570
Spline	0.44	8.78	0.84	158	−0.19	5.46	0.75	697	0.37	4.52	1.05	300
B. OTM put (0.85<Moneyness<1)
SVI	3.03	5.86	2.44	2,221	4.36	5.90	3.52	2,217	1.64	3.27	3.75	1,092
Spline	0.13	3.72	1.89	2,209	0.39	2.44	1.99	2,164	0.39	2.29	2.72	1,069
C. OTM call (1<Moneyness<1.15)
SVI	1.08	5.16	2.26	2,520	1.96	3.71	3.57	2,191	0.59	2.56	3.47	767
Spline	0.02	2.90	1.84	2,643	0.12	1.62	2.44	2,245	0.06	1.37	2.18	1,031
D. Deep OTM call (Moneyness>1.15)
SVI	0.24	8.76	1.49	389	−0.94	4.92	2.08	669	0.16	3.14	2.66	163
Spline	−0.13	3.93	0.60	436	−0.22	2.30	0.92	884	0.41	1.97	1.60	238

Model	Short (10–90 days)				Medium (91–180 days)				Long (>180 days)
Model	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	−6.92	13.17	1.06	234	−1.01	11.27	1.88	826	−0.07	4.88	1.80	570
Spline	0.44	8.78	0.84	158	−0.19	5.46	0.75	697	0.37	4.52	1.05	300
B. OTM put (0.85<Moneyness<1)
SVI	3.03	5.86	2.44	2,221	4.36	5.90	3.52	2,217	1.64	3.27	3.75	1,092
Spline	0.13	3.72	1.89	2,209	0.39	2.44	1.99	2,164	0.39	2.29	2.72	1,069
C. OTM call (1<Moneyness<1.15)
SVI	1.08	5.16	2.26	2,520	1.96	3.71	3.57	2,191	0.59	2.56	3.47	767
Spline	0.02	2.90	1.84	2,643	0.12	1.62	2.44	2,245	0.06	1.37	2.18	1,031
D. Deep OTM call (Moneyness>1.15)
SVI	0.24	8.76	1.49	389	−0.94	4.92	2.08	669	0.16	3.14	2.66	163
Spline	−0.13	3.93	0.60	436	−0.22	2.30	0.92	884	0.41	1.97	1.60	238

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. $P^{\mod}$ ⁠: option price via binomial tree (with the Trigeorgis parametrization and 500 steps) 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

[ViewLarge]

Sharing Unavailable