Table 3.

Statistics of the calibrated values and of the mean absolute percentage error (goodness of fit) for the credit risk model in Cathcart and El-Jahel (2003), formula ${\mathrm{\Pi }}_{{}_{\mathit{CIR}}}$, and for its revised version here proposed, formula ${\mathrm{\Pi }}_{{}_V}$

			$\frac{x_0}{x_L}$	$\alpha$	${\sigma }_x$	a	b	MAPE %
(AAA) – (A-)	${\mathrm{\Pi }}_{\mathit{CIR}}$	Average	3.224	0.054	0.237	0.010	1.516	$8.53\%$
		Min	2.392	0.023	0.177	$-0.013$	$-2.752$	$2.39\%$
		Max	4.715	0.120	0.300	0.010	1.873	$19.20\%$
		SD	0.589	0.020	0.032	0.003	0.667	$2.48\%$
	${\mathrm{\Pi }}_V$	Average	3.224	0.054	0.237	0.010	1.506	$8.52\%$
		Min	2.392	0.022	0.177	$-0.013$	$-2.804$	$2.25\%$
		Max	4.716	0.121	0.300	0.010	1.860	$19.23\%$
		SD	0.588	0.020	0.032	0.003	0.672	$2.51\%$
(BBB+) – (BBB-)	${\mathrm{\Pi }}_{\mathit{CIR}}$	Average	3.002	0.037	0.236	0.009	1.285	$8.10\%$
		Min	1.612	0.009	0.101	$-0.009$	$-3.832$	$0.90\%$
		Max	5.076	0.191	0.300	0.010	1.832	$15.73\%$
		SD	0.569	0.024	0.030	0.003	1.069	$2.81\%$
	${\mathrm{\Pi }}_V$	Average	2.999	0.037	0.236	0.009	1.277	$8.06\%$
		Min	1.612	0.009	0.101	$-0.009$	$-3.881$	$0.31\%$
		Max	4.977	0.188	0.300	0.010	1.822	$15.76\%$
		SD	0.558	0.023	0.030	0.003	1.075	$2.92\%$
(BB+) – (CCC)	${\mathrm{\Pi }}_{\mathit{CIR}}$	Average	2.589	0.085	0.243	0.005	$-3.392$	$6.79\%$
		Min	1.015	$-0.029$	0.115	$-0.020$	$-19.872$	$3.42\%$
		Max	5.035	1.314	0.294	0.010	1.639	$10.41\%$
		SD	0.849	0.317	0.047	0.010	7.282	$2.18\%$
	${\mathrm{\Pi }}_V$	Average	2.583	0.084	0.244	0.005	$-3.434$	$5.70\%$
		Min	1.015	$-0.030$	0.114	$-0.020$	$-19.946$	$1.86\%$
		Max	4.936	1.304	0.300	0.010	1.638	$10.19\%$
		SD	0.831	0.315	0.047	0.010	7.351	$2.39\%$

For each one of the 142 European companies listed in Appendix C, the parameters are calibrated by employing CDS spreads with maturities 6 months and 1, 2, 3, 4, 5, 7, 10, 20 and 30 years. The CDS spreads are quoted on February 3, 2020. Companies are organized in three groups according to their S&P rating. The first group is made of 57 companies characterized by medium and high investment grade, that is credit rating greater than or equal to $A-$. The second group is made of 68 companies characterized by low investment grade, that is credit rating in the range $BBB+$ and $BBB-$. The third group is made of 17 companies characterized by speculative (no investment) grade, that is credit rating lower than $BBB-$. The statistics of the calibrations are available for each one of these three groups