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

Table 5: Results of the parameter estimations for the processes r and w in the
model of Bakshi, Madan and Zhang using non-defaultable weekly bond data
from October 1, 1993, until June 1, 2001.
a r 0.1148954
ρ r,w -0.3162099
σ r 0.01131460
θ w 0.001181332
a w 0.1827164
σ w 0.003770599
â r 0.02235351
â w 0.4031626
Table 6: Results of the parameter estimations for the processes s and u in
the model of Bakshi, Madan and Zhang using defaultable weekly bond data of
American Industrials for the two rating classes BBB1 and A2 from October 1,
1993, until June 1, 2001.
BBB1 A2
a u 0.8319099 0.6573920
σ u 0.002652917 0.002251548
θ u 0.0006284389 0.0005292102
ρ r,u 0.5860846 0.5578109
Λ r 0.8334248 0.8665440
â u 2.573223·10 −6 3.151313·10 −6
If we estimate the parameters using the data speciÞed in Section 2, by application
of Kalman Þlter techniques we get the estimates as speciÞed in Tables
5and6.
Based on these parameter estimates we can calculate the mean reversion levels
of the stochastic processes. For w we get 0.65%, for r we get an average mean
reversion level of 5.62%. This value is quite intuitive as the average observed
3-month rate is approximately 5.12%. For rating categories BBB1 and A2 the
mean reversion levels of u are 8 bp, 8 bp, and for s 81 bp, 57 bp, respectively.
These numbers are rather intuitive as the average 3-month spreads for rating
categories BBB1 and A2 approximately equal 76 bp and 59 bp, respectively,
i.e. decrease for ratings of higher quality.
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