On models of default risk. (Q2707142)

From the introduction: We try to understand the links between a ``default-free'' world and a defaultable one. We recall some well-known, though perhaps forgotten, tools to compute this expectation and simplify most of the proofs in the mathematical finance literature. We make precise the relation between the default time and the price's filtration.NEWLINENEWLINE In the first part we recall that if the information is only the time when the default appears, the computation of the expectation of a defaultable payoff involves the intensity oft the default process, which can be explicitly defined in terms of the distribution function \(\tau\). [\dots]NEWLINENEWLINE In a second part, we assume that the information of the agent at time \(t\) consists of knowledge of the behaviour of the prices up to time \(t\) as well as the default time. We show that, in this case, the results depend strongly on the stochastic link between the asset process and the default time. In particular, we show that the intensity does not provide sufficient information about this stochastic link. We use some tolls from the theory of enlargement of filtrations to compute the intensity of the default time when it exists.