Table 12 Out-of-sample pricing errors of...

Table 12

Out-of-sample pricing errors of CSI 300 index options from January 4, 2021 to December 31, 2021

	Short (10–90 days)				Long (>90 days)
	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	31.38	45.32	3.35	701	26.78	29.87	12.81	861
Spline	1.66	18.86	1.63	719	14.75	17.22	11.28	1,181
Linear	0.61	16.15	1.19	719	12.49	14.35	8.19	1,181
iCubic	2.56	14.99	1.17	719	12.81	14.44	8.21	1,181
B. OTM put (0.85<Moneyness<1)
SVI	10.56	21.72	12.82	6,805	−0.66	15.60	29.55	1,800
Spline	4.82	14.29	8.30	7,319	4.08	12.26	27.14	4,714
Linear	5.30	12.51	7.63	7,319	8.13	9.75	22.48	4,769
iCubic	5.43	12.47	7.72	7,319	8.23	9.77	23.07	4,769
C. OTM call (1<Moneyness<1.15)
SVI	10.12	20.88	11.37	4,250	−0.69	16.48	30.72	1,067
Spline	−1.96	15.43	10.73	4,562	3.64	17.32	36.84	2,827
Linear	−4.64	12.53	8.54	4,562	−7.31	12.12	28.83	2,857
iCubic	−4.67	12.39	8.60	4,562	−7.81	12.18	29.52	2,857
D. Deep OTM call (Moneyness>1.15)
SVI	−7.87	27.19	2.30	797	−13.61	20.40	11.10	465
Spline	−15.87	23.36	2.57	834	−19.90	22.56	13.35	1,156
Linear	−10.70	18.45	2.04	834	−11.40	13.78	8.64	1,156
iCubic	−7.61	15.86	1.85	834	−10.39	12.87	8.07	1,156

	Short (10–90 days)				Long (>90 days)
	MPE (%)	MAE (%)	RMSE	N	MPE (%)	MAE (%)	RMSE	N
A. Deep OTM put (Moneyness<0.85)
SVI	31.38	45.32	3.35	701	26.78	29.87	12.81	861
Spline	1.66	18.86	1.63	719	14.75	17.22	11.28	1,181
Linear	0.61	16.15	1.19	719	12.49	14.35	8.19	1,181
iCubic	2.56	14.99	1.17	719	12.81	14.44	8.21	1,181
B. OTM put (0.85<Moneyness<1)
SVI	10.56	21.72	12.82	6,805	−0.66	15.60	29.55	1,800
Spline	4.82	14.29	8.30	7,319	4.08	12.26	27.14	4,714
Linear	5.30	12.51	7.63	7,319	8.13	9.75	22.48	4,769
iCubic	5.43	12.47	7.72	7,319	8.23	9.77	23.07	4,769
C. OTM call (1<Moneyness<1.15)
SVI	10.12	20.88	11.37	4,250	−0.69	16.48	30.72	1,067
Spline	−1.96	15.43	10.73	4,562	3.64	17.32	36.84	2,827
Linear	−4.64	12.53	8.54	4,562	−7.31	12.12	28.83	2,857
iCubic	−4.67	12.39	8.60	4,562	−7.81	12.18	29.52	2,857
D. Deep OTM call (Moneyness>1.15)
SVI	−7.87	27.19	2.30	797	−13.61	20.40	11.10	465
Spline	−15.87	23.36	2.57	834	−19.90	22.56	13.35	1,156
Linear	−10.70	18.45	2.04	834	−11.40	13.78	8.64	1,156
iCubic	−7.61	15.86	1.85	834	−10.39	12.87	8.07	1,156

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 (modified for known cash dividends) with a volatility forecated from the previous trading day. N: number of out-of-sample options

Source(s): Authors’ own work

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