13,295 research outputs found
Modelling the Dynamic Relationship between Systematic Default and Recovery Risk
Default correlation modelling is becoming the most popular problem in the
field of credit derivatives pricing. An increase in default risk would cause the
recovery rate to change correspondingly. Correlation between default and
recovery rates has a noticeable effect on risk measures and credit derivatives
pricing.
After an introduction, we review the most recent literature covering default
correlation and the relationship between default and recovery rates. We
adopt the copula methodology to focus on estimating the default correlations
rather than focus on modelling probabilities of default, we then use stress
testing to compare the distributions of the probability of default under different
copula functions. We develop a Gamma-Beta model to link the recovery
rate directly with the individual probability of default, this is instead of an
extended one factor model to relate them by a systematic common factor.
One factor models are re-examined to explore correlated recovery rates under
three distributions: the Logit-normal, the Normal and the Log-normal. By
analyzing the results respectively obtained from these two classes of modelling
scheme, we argue that the direct dependence (Gamma-Beta) model
behaves better, in estimating the recovery rate given individual probability
of default and in suggesting a better indication of their relationship. Finally,
we apply default correlation and the correlated recovery rate to portfolio risk
modelling. We conclude that if the recovery rates are independent stochastic
variables, the expected losses in a large portfolio might be underestimated
because the uncorrelated recovery risks can be diversified, so the correlation
between default rate and recovery risk can not be neglected in the applications.
Here, we believe the first time, the recovery rate depends on individual
default probability by means of a closed formula
Hard X-ray emission cutoff in anomalous X-ray pulsar 4U 0142+61 detected by INTEGRAL
The anomalous X-ray pulsar 4U 0142+61 was studied by the INTEGRAL
observations. The hard X-ray spectrum of 18 -- 500 keV for 4U 0142+61 was
derived using near 9 years of INTEGRAL/IBIS data. We obtained the average hard
X-ray spectrum of 4U 0142+61 with all available data. The spectrum of 4U
0142+61 can be fitted with a power-law with an exponential high energy cutoff.
This average spectrum is well fitted with a power-law of plus a cutoff energy at keV. The hard X-ray flux of the
source from 20 -- 150 keV showed no significant variations (within 20) from
2003 -- 2011. The spectral profiles have some variability in nine years: photon
index varied from 0.3 -- 1.5, and cutoff energies of 110 -- 250 keV. The
detection of the high energy cutoff around 130 keV shows some constraints on
the radiation mechanisms of magnetars and possibly probes the differences
between magnetar and accretion models for these special class of neutron stars.
Future HXMT observations could provide stronger constraints on the hard X-ray
spectral properties of this source and other magnetar candidates.Comment: 9 pages, 5 figures, 2 tables, figures are updated, new data are
added, conclusion does not change, to be published in RA
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