Option Pricing Model Combining Ensemble Learning Methods and Network Learning Structure

Table 3

Out-of-sample RMSE for Model 3 in terms of moneyness and time to maturity.

	Model	All	DITM	ITM	ATM	OTM	DOTM
ALL	BS	2.808	4.997	1.674	3.440	4.585	2.898
	Heston	2.831	4.121	1.887	3.446	4.482	2.238
	DNN	0.030	0.398	0.051	0.063	0.322	0.202
	XGBoost	0.027	0.288	0.020	0.048	0.133	0.215
	LightGBM	0.025	0.281	0.026	0.043	0.161	0.214
	Ours	0.016	0.280	0.019	0.027	0.086	0.090
Short term	BS	2.538	4.930	2.560	4.632	4.359	2.385
	Heston	2.607	4.101	2.969	4.135	4.257	2.097
	DNN	0.062	0.386	0.234	0.346	0.349	0.340
	XGBoost	0.042	0.302	0.022	0.260	0.181	0.133
	LightGBM	0.041	0.255	0.027	0.211	0.177	0.133
	Ours	0.025	0.248	0.023	0.113	0.117	0.133
Medium term	BS	2.500	4.113	2.497	1.945	2.789	2.317
	Heston	2.811	4.864	2.793	1.942	2.177	1.980
	DNN	0.062	0.144	0.285	0.302	0.386	0.179
	XGBoost	0.047	0.076	0.149	0.092	0.289	0.038
	LightGBM	0.043	0.072	0.149	0.093	0.238	0.034
	Ours	0.034	0.036	0.149	0.092	0.178	0.020
Long term	BS	2.248	—	3.234	3.336	4.160	3.116
	Heston	2.158	—	3.602	3.306	4.265	2.719
	DNN	0.273	—	0.536	0.514	0.773	0.397
	XGBoost	0.140	—	0.385	0.389	0.423	0.463
	LightGBM	0.152	—	0.371	0.385	0.456	0.465
	Ours	0.151	—	0.311	0.366	0.411	0.282