We model the term structure of the forward default intensity and the default
density by using L\'evy random fields, which allow us to consider the credit
derivatives with an after-default recovery payment. As applications, we study
the pricing of a defaultable bond and represent the pricing kernel as the
unique solution of a parabolic integro-differential equation. Finally, we
illustrate by numerical examples the impact of the contagious jump risks on the
defaultable bond price in our model.
We study the pricing of credit derivatives with asymmetric information. The
managers have complete information on the value process of the firm and on the
default threshold, while the investors on the market have only partial
observations, especially about the default threshold. Different information
structures are distinguished using the framework of enlargement of filtrations.
We specify risk neutral probabilities and we evaluate default sensitive
contingent claims in these cases.
We study multiple defaults where the global market information is modelled as
progressive enlargement of filtrations. We shall provide a general pricing
formula by establishing a relationship between the enlarged filtration and the
reference default-free filtration in the random measure framework. On each
default scenario, the formula can be interpreted as a Radon-Nikodym derivative
of random measures.