162 research outputs found
Thin times and random times' decomposition
The paper studies thin times which are random times whose graph is contained
in a countable union of the graphs of stopping times with respect to a
reference filtration . We show that a generic random time can be
decomposed into thin and thick parts, where the second is a random time
avoiding all -stopping times. Then, for a given random time ,
we introduce , the smallest right-continuous filtration
containing and making a stopping time, and we show that, for
a thin time , each -martingale is an -semimartingale, i.e., the hypothesis for
holds. We present applications to honest times,
which can be seen as last passage times, showing classes of filtrations which
can only support thin honest times, or can accommodate thick honest times as
well
Dynamics of multivariate default system in random environment
We consider a multivariate default system where random environmental
information is available. We study the dynamics of the system in a general
setting and adopt the point of view of change of probability measures. We also
make a link with the density approach in the credit risk modelling. In the
particular case where no environmental information is concerned, we pay a
special attention to the phenomenon of system weakened by failures as in the
classical reliability system
Valuation of default sensitive claims under imperfect information.
We propose an evaluation method for financial assets subject to default risk, when investors face imperfect information about the state variable triggering the default. The model we propose generalizes the one by Duffie and Lando (2001) in the following way:(i)it incorporates informational noise in continuous time, (ii) it respects the (H) hypothesis, (iii) it precludes arbitrage from insiders. The model is sufficiently general to encompass a large class of structural models. In this setting we show that the default time is totally inaccessible in the market’s filtration and derive the martingale hazard process. Finally, we provide pricing formulas for default-sensitive claims and illustrate with particular examples the shapes of the credit spreads and the conditional default probabilities. An important feature of the conditional default probabilities is they are non Markovian. This might shed some light on observed phenomena such as the ”rating momentum”.hybrid models; default sensitive claims;
What happens after a default: the conditional density approach
We present a general model for default time, making precise the role of the
intensity process, and showing that this process allows for a knowledge of the
conditional distribution of the default only "before the default". This lack of
information is crucial while working in a multi-default setting. In a single
default case, the knowledge of the intensity process does not allow to compute
the price of defaultable claims, except in the case where immersion property is
satisfied. We propose in this paper the density approach for default time. The
density process will give a full characterization of the links between the
default time and the reference filtration, in particular "after the default
time". We also investigate the description of martingales in the full
filtration in terms of martingales in the reference filtration, and the impact
of Girsanov transformation on the density and intensity processes, and also on
the immersion property
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