Table 7.

Calibration of formulas ${\mathrm{\Pi }}_{\mathit{CIR}}$ and ${\mathrm{\Pi }}_V$ for a selected group of companies

Rating	Company	Model	$\frac{x_0}{x_L}$	$\alpha$	${\sigma }_x$	a	b	MAPE %
AA	Allianz SE	${\mathrm{\Pi }}_{\mathit{CIR}}$	3.505	0.064	0.247	0.010	1.673	$9.16\%$
		${\mathrm{\Pi }}_V$	3.506	0.064	0.247	0.010	1.665	$9.18\%$
AA-	Shell PLC	${\mathrm{\Pi }}_{\mathit{CIR}}$	2.941	0.041	0.219	0.010	1.790	$11.20\%$
		${\mathrm{\Pi }}_V$	2.940	0.041	0.219	0.010	1.775	$11.22\%$
A+	BNP Paribas SA	${\mathrm{\Pi }}_{\mathit{CIR}}$	4.405	0.086	0.300	0.010	1.647	$10.74\%$
		${\mathrm{\Pi }}_V$	4.406	0.086	0.300	0.010	1.634	$10.75\%$
A	Banco Santander SA	${\mathrm{\Pi }}_{\mathit{CIR}}$	2.743	0.052	0.214	0.010	1.669	$6.68\%$
		${\mathrm{\Pi }}_V$	2.743	0.052	0.214	0.010	1.660	$6.70\%$
A-	Daimler AG	${\mathrm{\Pi }}_{\mathit{CIR}}$	2.600	0.023	0.210	0.010	1.456	$6.63\%$
		${\mathrm{\Pi }}_V$	2.600	0.023	0.210	0.010	1.443	$6.65\%$
BBB+	Deutsche Telekom AG	${\mathrm{\Pi }}_{\mathit{CIR}}$	3.860	0.074	0.292	0.010	1.690	$7.58\%$
		${\mathrm{\Pi }}_V$	3.860	0.074	0.292	0.010	1.683	$7.59\%$
BBB	Banco Sabadell SA	${\mathrm{\Pi }}_{\mathit{CIR}}$	2.929	0.042	0.262	0.010	1.350	$9.37\%$
		${\mathrm{\Pi }}_V$	2.927	0.042	0.262	0.010	1.345	$9.38\%$
BBB-	Edison SpA	${\mathrm{\Pi }}_{\mathit{CIR}}$	2.600	0.042	0.216	0.010	1.583	$4.60\%$
		${\mathrm{\Pi }}_V$	2.599	0.042	0.216	0.010	1.573	$4.60\%$
BB+	Leonardo SpA	${\mathrm{\Pi }}_{\mathit{CIR}}$	2.710	0.020	0.237	0.010	1.600	$7.55\%$
		${\mathrm{\Pi }}_V$	2.712	0.020	0.237	0.010	1.601	$7.54\%$
B	Selecta BV	${\mathrm{\Pi }}_{\mathit{CIR}}$	2.441	$-0.006$	0.265	0.010	0.629	$4.84\%$
		${\mathrm{\Pi }}_V$	2.444	$-0.006$	0.266	0.010	0.686	$4.85\%$

The calibration is performed by fitting the curves of CDS spreads. Maturities: 6 months and 1, 2, 3, 5, 7, 10, 20 and 30 years. The CDS spreads used are quoted on February 3, 2020. The CDSs employed have the following features. Restructuring clause: XR14. Seniority: Senior unsecured. The rating is by S&P. ${\mathrm{\Pi }}_{\mathit{CIR}}$ indicates the credit risk model in Cathcart and El-Jahel (2003), that is theoretical values obtained using formula (22). ${\mathrm{\Pi }}_V$ indicates the valuation framework here proposed, that is theoretical values obtained using formula (21). Thomson Reuters Eikon is our data provider. The calibrated values for all the other companies considered in the analysis are not reported for brevity, and are available upon request