Polynomial Chaos Expansion Approach to Interest Rate Models

Table 21

Evaluation of first six orthonormal Hermite polynomials on the vector of equally spaced points from to .

−2.00000	1.00000	−2.82843	4.94975	4.94975	3.87836	0.25820
−1.89744	1.00000	−2.68338	4.38443	4.38443	2.37691	1.26342
−1.79487	1.00000	−2.53833	3.84887	3.84887	1.19518	1.83459
−1.69231	1.00000	−2.39328	3.34307	3.34307	0.29413	2.06903
−1.58974	1.00000	−2.24824	2.86701	2.86701	−0.36308	2.05174
−1.48718	1.00000	−2.10319	2.42071	2.42071	−0.81117	1.85611
−1.38462	1.00000	−1.95814	2.00417	2.00417	−1.08266	1.54464
−1.28205	1.00000	−1.81309	1.61737	1.61737	−1.20789	1.16962
−1.17949	1.00000	−1.66805	1.26033	1.26033	−1.21508	0.77387
−1.07692	1.00000	−1.52300	0.93305	0.93305	−1.13023	0.39138
−0.97436	1.00000	−1.37795	0.63551	0.63551	−0.97719	0.04808
−0.87179	1.00000	−1.23290	0.36773	0.36773	−0.77766	−0.23748
−0.76923	1.00000	−1.08786	0.12971	0.12971	−0.55115	−0.45346
−0.66667	1.00000	−0.94281	−0.07857	−0.07857	−0.31501	−0.59396
−0.56410	1.00000	−0.79776	−0.25709	−0.25709	−0.08441	−0.65840
−0.46154	1.00000	−0.65271	−0.40585	−0.40585	0.12764	−0.65073
−0.35897	1.00000	−0.50767	−0.52487	−0.52487	0.31028	−0.57879
−0.25641	1.00000	−0.36262	−0.61413	−0.61413	0.45486	−0.45358
−0.15385	1.00000	−0.21757	−0.67363	−0.67363	0.55485	−0.28856
−0.05128	1.00000	−0.07252	−0.70339	−0.70339	0.60594	−0.09896
0.05128	1.00000	0.07252	−0.70339	−0.70339	0.60594	0.09896
0.15385	1.00000	0.21757	−0.67363	−0.67363	0.55485	0.28856
0.25641	1.00000	0.36262	−0.61413	−0.61413	0.45486	0.45358
0.35897	1.00000	0.50767	−0.52487	−0.52487	0.31028	0.57879
0.46154	1.00000	0.65271	−0.40585	−0.40585	0.12764	0.65073
0.56410	1.00000	0.79776	−0.25709	−0.25709	−0.08441	0.65840
0.66667	1.00000	0.94281	−0.07857	−0.07857	−0.31501	0.59396
0.76923	1.00000	1.08786	0.12971	0.12971	−0.55115	0.45346
0.87179	1.00000	1.23290	0.36773	0.36773	−0.77766	0.23748
0.97436	1.00000	1.37795	0.63551	0.63551	−0.97719	−0.04808
1.07692	1.00000	1.52300	0.93305	0.93305	−1.13023	−0.39138
1.17949	1.00000	1.66805	1.26033	1.26033	−1.21508	−0.77387
1.28205	1.00000	1.81309	1.61737	1.61737	−1.20789	−1.16962
1.38462	1.00000	1.95814	2.00417	2.00417	−1.08266	−1.54464
1.48718	1.00000	2.10319	2.42071	2.42071	−0.81117	−1.85611
1.58974	1.00000	2.24824	2.86701	2.86701	−0.36308	−2.05174
1.69231	1.00000	2.39328	3.34307	3.34307	0.29413	−2.06903
1.79487	1.00000	2.53833	3.84887	3.84887	1.19518	−1.83459
1.89744	1.00000	2.68338	4.38443	4.38443	2.37691	−1.26342
2.00000	1.00000	2.82843	4.94975	4.94975	3.87836	−0.25820