Table 13 Out-of-sample pricing errors of...

Table 13

Out-of-sample pricing errors of soybean meal futures options from January 4, 2021 to December 31, 2021

	Short (10–90 days)				Medium (91–180 days)				Long (>180 days)
	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	−6.18	17.24	1.46	215	0.52	14.27	2.36	627	3.90	9.91	4.83	373
Spline	−9.50	15.03	1.31	136	−4.33	12.89	1.50	505	4.11	16.76	3.67	158
Linear	−8.76	13.78	1.16	136	−4.32	12.87	1.54	505	3.35	16.57	3.68	158
iCubic	−6.29	12.55	1.10	136	4.26	17.64	11.57	490	3.49	16.75	3.83	158
B. OTM put (0.85<Moneyness<1)
SVI	7.45	11.97	3.91	2,205	6.04	7.97	5.05	1,864	2.51	6.16	6.80	744
Spline	−0.74	10.35	3.51	2,051	0.94	5.07	3.08	1,791	0.23	6.35	6.77	683
Linear	−0.37	9.77	3.33	2,051	1.48	5.29	3.72	1,791	1.54	5.64	5.99	683
iCubic	−0.35	9.67	3.36	2,040	1.73	5.68	4.43	1,760	2.30	6.33	8.05	683
C. OTM call (1<Moneyness<1.15)
SVI	6.36	11.37	4.21	2,305	3.59	5.89	5.24	1,794	1.63	5.61	7.86	438
Spline	−0.14	9.45	4.38	2,402	0.18	4.23	4.78	1,869	−0.71	3.86	5.47	688
Linear	0.38	9.77	4.22	2,402	0.46	4.23	5.06	1,869	−0.32	3.78	5.25	688
iCubic	0.26	9.67	4.18	2,388	0.41	4.20	4.76	1,846	−0.31	3.88	5.96	688
D. Deep OTM call (Moneyness>1.15)
SVI	3.80	16.02	2.48	341	0.63	8.06	3.31	546	1.13	5.37	4.16	109
Spline	−7.35	14.03	1.88	393	−1.41	6.56	2.27	719	−2.47	6.06	4.64	158
Linear	−7.82	14.24	1.88	393	−1.11	6.70	2.26	719	−2.31	6.08	4.86	158
iCubic	−4.07	13.79	1.98	388	−0.34	6.97	2.53	711	−1.57	6.59	5.37	158

	Short (10–90 days)				Medium (91–180 days)				Long (>180 days)
	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	−6.18	17.24	1.46	215	0.52	14.27	2.36	627	3.90	9.91	4.83	373
Spline	−9.50	15.03	1.31	136	−4.33	12.89	1.50	505	4.11	16.76	3.67	158
Linear	−8.76	13.78	1.16	136	−4.32	12.87	1.54	505	3.35	16.57	3.68	158
iCubic	−6.29	12.55	1.10	136	4.26	17.64	11.57	490	3.49	16.75	3.83	158
B. OTM put (0.85<Moneyness<1)
SVI	7.45	11.97	3.91	2,205	6.04	7.97	5.05	1,864	2.51	6.16	6.80	744
Spline	−0.74	10.35	3.51	2,051	0.94	5.07	3.08	1,791	0.23	6.35	6.77	683
Linear	−0.37	9.77	3.33	2,051	1.48	5.29	3.72	1,791	1.54	5.64	5.99	683
iCubic	−0.35	9.67	3.36	2,040	1.73	5.68	4.43	1,760	2.30	6.33	8.05	683
C. OTM call (1<Moneyness<1.15)
SVI	6.36	11.37	4.21	2,305	3.59	5.89	5.24	1,794	1.63	5.61	7.86	438
Spline	−0.14	9.45	4.38	2,402	0.18	4.23	4.78	1,869	−0.71	3.86	5.47	688
Linear	0.38	9.77	4.22	2,402	0.46	4.23	5.06	1,869	−0.32	3.78	5.25	688
iCubic	0.26	9.67	4.18	2,388	0.41	4.20	4.76	1,846	−0.31	3.88	5.96	688
D. Deep OTM call (Moneyness>1.15)
SVI	3.80	16.02	2.48	341	0.63	8.06	3.31	546	1.13	5.37	4.16	109
Spline	−7.35	14.03	1.88	393	−1.41	6.56	2.27	719	−2.47	6.06	4.64	158
Linear	−7.82	14.24	1.88	393	−1.11	6.70	2.26	719	−2.31	6.08	4.86	158
iCubic	−4.07	13.79	1.98	388	−0.34	6.97	2.53	711	−1.57	6.59	5.37	158

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