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

Table 6

OEX put prices computed using the previous 260 daily closing prices of the S&P 100 Index.

Moneyness ↓	Maturity	Short			Medium			Long
	Method	CLM	FD	BT	CLM	FD	BT	CLM	FD	BT
DOTM	RMSE	2.273	2.719	2.756	3.135	4.433	4.398	3.261	4.353	4.686
	MPE	−1.259	−1.801	−2.047	−2.137	−3.126	−3.043	−0.790	−3.202	−2.189
	MAE (%)	38.729	46.864	45.730	33.700	48.657	46.497	20.886	36.821	37.523
	Number of puts	30113			19535			3721
OTM	RMSE	3.246	4.750	4.983	3.139	5.769	6.690	4.920	4.939	6.851
	MPE	−2.171	−3.731	−1.601	−1.445	−3.732	−4.858	3.392	−2.135	0.337
	MAE (%)	22.300	33.979	35.479	23.264	22.936	22.134	13.171	12.950	14.277
	Number of puts	26243			15392			3630
ITM	RMSE	2.509	3.341	3.059	3.269	3.956	4.869	6.754	5.018	6.138
	MPE	−0.266	−1.674	−1.601	1.221	−0.930	−0.161	4.661	2.160	1.979
	MAE (%)	5.893	6.079	5.154	5.750	5.793	7.731	10.857	6.550	9.439
	Number of puts	26066			14624			3692
DITM	RMSE	1.926	2.192	2.223	2.225	2.404	2.685	9.713	7.389	8.264
	MPE	−0.778	−0.776	−0.794	0.388	0.452	0.899	7.732	5.886	8.805
	MAE (%)	1.071	1.179	1.260	1.243	1.429	2.510	4.320	3.786	3.809
	Number of puts	35458			22315			7341

Note. This table reports the empirical results for OEX 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.