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

Table 7

IBM put prices computed using the previous 130 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	0.523	0.582	0.576	0.785	1.076	0.964	0.946	1.201	1.352
	MPE	−0.343	−0.405	−0.386	−0.601	−0.837	−0.812	−0.346	−0.978	−1.025
	MAE (%)	50.542	61.532	58.125	47.394	57.690	55.328	41.266	55.452	57.023
	Number of puts	6156			7852			5230
OTM	RMSE	1.050	1.281	1.303	1.185	1.788	1.536	1.786	1.929	1.953
	MPE	−0.492	−0.935	−0.985	−0.575	−1.475	−1.432	0.049	−1.340	−1.029
	MAE (%)	28.508	38.416	39.852	20.634	33.875	31.652	18.775	25.875	24.851
	Number of puts	4966			4824			3527
ITM	RMSE	0.901	0.982	0.975	1.236	1.302	1.403	2.188	1.890	2.065
	MPE	0.042	−0.460	−0.421	0.258	−0.722	−0.627	0.928	−0.534	−0.865
	MAE (%)	8.233	8.216	8.202	7.286	8.766	9.013	10.316	10.016	10.287
	Number of puts	5171			5011			3676
DITM	RMSE	0.459	0.950	0.926	0.941	0.537	0.621	2.197	1.330	1.853
	MPE	0.152	−0.080	−0.126	0.608	0.120	0.356	1.501	0.519	1.026
	MAE (%)	1.026	1.213	1.326	1.653	1.266	1.401	5.133	4.266	4.813
	Number of puts	8033			9864			8111

Note. This table reports the empirical results for IBM puts using the previous 130 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.