Empirical Evaluation of Hybrid Defaultable Bond Pricing ... - risklab

Table 10: Average R 2 values (out—of-sample) of the different models based on
data from October 1, 1993, to June 1, 2001.
Rating Class SZ Ext. SZ Bakshi et al
Industrials BBB1 0.394 0.416 0.326
Industrials A2 0.300 0.422 0.264
Treasury Strips 0.737 0.769 0.824
of modeling the structural differences of bond prices through time. This
is caused by the greater ßexibility of the spread process. Our empirical
analysis shows that the short rate spread s has a higher correlation with
short rate interest rates, whereas the uncertainty index u has a higher
correlation with long term interest rates (see Table 12).
Table 11: Correlations of the processes s and u in the model of Schmid and
Zagst with the observed BBB1 spreads for different maturities.
Observed spreads with maturities (in years)
0.25 0.5 1 2 3 4 5 7 10 20 30
s 0.84 0.89 0.82 0.62 0.55 0.47 0.46 0.42 0.44 0.39 0.42
u 0.61 0.63 0.83 0.94 0.97 0.96 0.99 0.99 0.98 0.98 0.98
Table 12: Correlations of the processes s and u in the extended model of Schmid
and Zagst with the observed BBB1 spreads for different maturities.
Observed spreads with maturities (in years)
0.25 0.5 1 2 3 4 5 7 10 20 30
s 0.84 0.90 0.86 0.69 0.62 0.53 0.53 0.49 0.50 0.45 0.48
u 0.63 0.65 0.84 0.94 0.97 0.96 0.98 0.99 0.98 0.99 0.98
• This result is further backed by the behavior of the functions C d (t, T )/(T −
t) and D d (t, T )/(T − t) (that basically show the dependence of S (t, T ) on
s and u) forÞxed t. While both functions converge to 0 as T tends to
∞, they show a different behavior in the time interval relevant for us (see
Figures 6 and 7): C d (t, T )/(T − t) is monotonically decreasing towards 0,
22