Credit models are increasingly interested in not just the probability of default, but in what happens to a credit on its way to default. Attention is being focused on the probability of moving from one credit level, or rating, to another. One convenient way of expressing this information is through a transition matrix. The primary source for these probabilities has been the rating agencies. As ...

For a given filtered probability space (Ω,F,P), where F = (Ft)t≥0 is a filtration, an F-adapted continuous increasing process Λ and a positive P-F local martingale N such that Zt := Nte−Λt ≤ 1, t ≥ 0, we construct a model of default time, i.e., a probability measure QZ and a random time τ on an extension of (Ω,F,P), such that Q[τ > t|Ft] = Zt, t ≥ 0. The probability QZ is linked with the well-k...

Default probability distributions are often defined in terms of their conditional default probability distribution, or their hazard rate. By their definition, they imply a unique probability density function. The applications of default probability distributions are varied, including the risk premium model used to price default bonds, reliability measurement models, insurance, etc. Fractional p...

In this paper, we investigate whether the theoretical default probability measures calculated from Merton’s (1974) structural credit risk model can provide a better way to explain and predict credit rating than traditional statistical models. The empirical results suggest that Merton’s theoretical default measure is not a sufficient statistic of equity market information concerning credit quali...

We present a semantics for adding uncertainty to conditional logics for default reasoning and be­ lief revision. We are able to treat conditional sen­ tences as statements of conditional probability, and express rules for revision such as "If A were believed, then B would be believed to degree p." This method of revision extends conditional­ ization by allowing meaningful revision by sen­ tence...

Global financial crises like the one recently experienced, affected both large and small institutions. Today, when there is heightened need for enhanced risk management tools, there are entities that are unable to employ sophisticated mechanisms due to limited data availability. Moreover, from the Basel II and Basel III point of view, Internal Ratings Based Approach requires that institutions h...

We study the behavior of diffusions coupled through their drifts in a way that each component mean-reverts to the mean of the ensemble. In particular, we are interested in the number of components reaching a “default” level in a given time. This coupling creates stability of the system in the sense that there is a large probability of “nearly no default” as opposed to the case of independent Br...

We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain. We reduce the partially observed stochastic control problem to a complete observati...