The paper deals with defaultable markets, one of the main research areas of mathematical finance. It proposes a new approach to the theory of such markets using techniques from the calculus of optional stochastic processes on unusual probability spaces, which was not presented before. The paper is a foundation paper and contains a number of fundamental results on modeling of defaultable markets...

Rating agencies are often subject to the criticism of being slow in adjusting their rating to current conditions. This paper examines the timeliness of rating changes and identifies factors which result in ’stickiness’ of rating actions. Stickiness is characterized by not adjusting the rating even when a market-based estimate of default probability changes. Introducing an extended econometric m...

In this paper we propose a framework for combining Disjunctive Logic Programming and Poole's Probabilistic Horn Abduction. We use the concept of hypothesis to spec­ ify the probability structure. We consider the case in which probabilistic information is not available. Instead of using probability intervals, we allow for the specification of the probabilities of disjunctions. Because mini­ mal ...

This paper investigates the information in corporate credit ratings from a positive and normative perspective. If ratings are to be informative indicators of credit risk they must reflect what a risk-averse investor cares about: both raw default probability and systematic risk. We find that ratings are inaccurate measures of raw default probability they are dominated as predictors of failure by...

In this paper we give a financial justification, based on non arbitrage conditions, of the (H) hypothesis in default time modelling. We also show how the (H) hypothesis is affected by an equivalent change of probability measure. The main technique used here is the theory of progressive enlargements of filtrations.

In this paper we ‘update’ the option implied probability of default (option iPoD) approach recently suggested in the literature. First, a numerically more stable objective function for the estimation of the risk neutral density is derived whose integrals can be solved analytically. Second, it is reasoned that the originally proposed approach for the estimation of the PoD has some serious drawba...

Imprecise Probability or Upper and Lower Prob ability is represented as a very simple but powerful logic Despite having a very di erent language from classical log ics it enjoys many of the most important properties which means that some extensions to classical logic can be applied in a fairly straightforward way The logic is extended to allow qualitative grades of belief which can be used to r...

The New Basel Capital Accord will allow the determination of banks’ regulatory capital requirements due to probabilities of default which are estimated and forecasted from internal ratings. Broadly, two rating philosophies are distinguished: Through the Cycle versus Point in Time Ratings. We employ a Likelihood-Ratio backtesting of both types with respect to their probability of default forecas...

We introduce an infectious default and recovery model for N obligors. The obligors are assumed to be exchangeable and their states are described by N Bernoulli-type random variables Si(i = 1, · · · , N). They are expressed by multiplying independent Bernoulli variables Xi, Yij and Y ′ ij , and the default and recovery infections are described by Yij and Y ′ ij . We obtain the default probabilit...

This paper proposes probabilistic default reasoning as a suitable approach to inheritance and recognition in uncertain and fuzzy object-oriented models. Firstly, we introduce an uncertain and fuzzy object-oriented model where a class property (i.e., an attribute or a method) can contain fuzzy sets interpreted as families of probability distributions, and uncertain class membership and property ...