Canonical Least-Squares Monte Carlo Valuation of American Options: Convergence and Empirical Pricing Analysis

Table 8

IBM put prices computed using the previous 260 daily closing prices of the IBM common stock.

Moneyness ↓	Maturity	Short			Medium			Long
	Method	CLM	FD	BT	CLM	FD	BT	CLM	FD	BT
DOTM	RMSE	0.564	0.615	0.609	0.980	1.189	1.077	1.001	1.478	1.629
	MPE	−0.386	−0.428	−0.419	−0.708	−0.885	−0.862	−0.772	−1.272	−1.319
	MAE (%)	52.825	64.323	60.354	47.885	59.715	52.893	41.816	62.002	65.120
	Number of puts	6156			7852			5230
OTM	RMSE	1.064	1.336	1.358	1.346	1.917	1.666	1.185	1.915	1.939
	MPE	−0.562	−0.993	−1.043	−0.651	−1.554	−1.511	−0.262	−1.603	−1.292
	MAE (%)	25.841	36.074	36.359	16.701	31.191	28.563	11.458	22.366	23.765
	Number of puts	4966			4824			3527
ITM	RMSE	0.888	1.011	1.004	1.230	1.416	1.517	1.511	1.474	1.649
	MPE	−0.039	−0.525	−0.486	0.194	−0.795	−0.702	0.621	−0.810	−1.141
	MAE (%)	7.856	8.407	8.324	8.169	8.364	8.536	9.391	7.216	10.137
	Number of puts	5171			5011			3676
DITM	RMSE	0.401	1.189	1.165	0.607	0.523	0.617	1.310	0.771	1.293
	MPE	0.075	−0.145	−0.191	0.310	−0.038	0.197	0.860	0.088	0.595
	MAE (%)	0.751	1.279	1.028	0.828	0.817	0.905	3.216	3.025	3.149
	Number of puts	8033			9864			8111

Note. This table reports the empirical results for IBM puts using the previous 260 daily closing prices as inputs. Each cell represents a particular combination of moneyness and time to maturity. The last row reports the number of options with corresponding combination. The remaining rows show the error statistic results of RMSE, MPE, and MAE.