Table 14 Out-of-sample pricing errors of...

Table 14

Out-of-sample pricing errors of copper futures options from November 2, 2020 to October 29, 2021

	Short (10–90 days)				Long (>90 days)
	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	21.34	57.23	38.54	541	9.42	30.89	64.78	549
Spline	−18.77	31.68	14.68	1,260	−5.06	20.02	39.19	603
Linear	−12.90	31.73	14.23	1,260	−1.50	21.92	41.67	603
iCubic	−7.95	33.31	16.88	1,260	−0.68	20.43	39.66	603
B. OTM put (0.85<Moneyness<1)
SVI	39.79	42.33	100.88	1,922	19.58	22.97	174.31	213
Spline	−0.01	14.37	60.83	2,443	0.28	12.67	191.20	250
Linear	−1.56	13.26	60.20	2,443	7.26	12.68	147.17	250
iCubic	−1.82	13.33	60.52	2,443	6.05	11.96	142.96	250
C. OTM call (1<Moneyness<1.15)
SVI	17.56	22.31	92.44	1,685	10.17	15.14	269.48	171
Spline	−0.91	13.42	83.69	1,945	−2.54	9.87	219.32	202
Linear	−0.05	13.03	82.15	1,945	−1.01	9.53	202.20	202
iCubic	0.35	13.36	83.20	1,945	−1.40	9.65	209.09	202
D. Deep OTM call (Moneyness>1.15)
SVI	10.62	31.79	34.03	135	32.44	38.22	392.26	13
Spline	−5.87	23.01	25.91	175	0.37	8.53	58.30	11
Linear	−4.82	23.39	26.04	175	0.36	8.72	59.09	11
iCubic	0.32	25.07	27.49	175	2.43	10.74	87.76	11

	Short (10–90 days)				Long (>90 days)
	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	21.34	57.23	38.54	541	9.42	30.89	64.78	549
Spline	−18.77	31.68	14.68	1,260	−5.06	20.02	39.19	603
Linear	−12.90	31.73	14.23	1,260	−1.50	21.92	41.67	603
iCubic	−7.95	33.31	16.88	1,260	−0.68	20.43	39.66	603
B. OTM put (0.85<Moneyness<1)
SVI	39.79	42.33	100.88	1,922	19.58	22.97	174.31	213
Spline	−0.01	14.37	60.83	2,443	0.28	12.67	191.20	250
Linear	−1.56	13.26	60.20	2,443	7.26	12.68	147.17	250
iCubic	−1.82	13.33	60.52	2,443	6.05	11.96	142.96	250
C. OTM call (1<Moneyness<1.15)
SVI	17.56	22.31	92.44	1,685	10.17	15.14	269.48	171
Spline	−0.91	13.42	83.69	1,945	−2.54	9.87	219.32	202
Linear	−0.05	13.03	82.15	1,945	−1.01	9.53	202.20	202
iCubic	0.35	13.36	83.20	1,945	−1.40	9.65	209.09	202
D. Deep OTM call (Moneyness>1.15)
SVI	10.62	31.79	34.03	135	32.44	38.22	392.26	13
Spline	−5.87	23.01	25.91	175	0.37	8.53	58.30	11
Linear	−4.82	23.39	26.04	175	0.36	8.72	59.09	11
iCubic	0.32	25.07	27.49	175	2.43	10.74	87.76	11

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. $P^{\mod}$ ⁠: Black-Scholes-Merton option price with a volatility forecasted from the previous trading day. N: number of out-of-sample options

Source(s): Authors’ own work

[ViewLarge]

Sharing Unavailable