Forecasting Credit Portfolio Risk

The main challenge of forecasting credit default risk in loan portfolios is forecasting the default probabilities and the default correlations. We derive a Merton-style threshold-value model for the default probability which treats the asset value of a firm as unknown and uses a factor model instead. In addition, we demonstrate how default correlations can be easily modeled. The empirical analysis is based on a large data set of German firms provided by Deutsche Bundesbank. We find that the inclusion of variables which are correlated with the business cycle improves the forecasts of default probabilities. Asset and default correlations depend on the factors used to model default probabilities. The better the point-in-time calibration of the estimated default probabilities, the smaller the estimated correlations. Thus, correlations and default probabilities should always be estimated simultaneously. --asset correlation,bank regulation,Basel II,credit risk,default correlation,default probability,logit model,probit model

Fragment size correlations in finite systems - application to nuclear multifragmentation

We present a new method for the calculation of fragment size correlations in a discrete finite system in which correlations explicitly due to the finite extent of the system are suppressed. To this end, we introduce a combinatorial model, which describes the fragmentation of a finite system as a sequence of independent random emissions of fragments. The sequence is accepted when the sum of the sizes is equal to the total size. The parameters of the model, which may be used to calculate all partition probabilities, are the intrinsic probabilities associated with the fragments. Any fragment size correlation function can be built by calculating the ratio between the partition probabilities in the data sample (resulting from an experiment or from a Monte Carlo simulation) and the 'independent emission' model partition probabilities. This technique is applied to charge correlations introduced by Moretto and collaborators. It is shown that the percolation and the nuclear statistical multifragmentaion model ({\sc smm}) are almost independent emission models whereas the nuclear spinodal decomposition model ({\sc bob}) shows strong correlations corresponding to the break-up of the hot dilute nucleus into nearly equal size fragments

Reconstruction of quantum theory on the basis of the formula of total probability

The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: ``first context and then probability.'' We start with the conventional formula of total probability for contextual (conditional) probabilities and then we rewrite it by eliminating combinations of incompatible contexts from consideration. In this way we obtain interference of probabilities without to appeal to the Hilbert space formalism or wave mechanics. However, we did not just reconstruct the probabilistic formalism of conventional quantum mechanics. Our contextual probabilistic model is essentially more general and, besides the projection to the complex Hilbert space, it has other projections. The most important new prediction is the possibility (at least theoretical) of appearance of hyperbolic interference

Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs

We study two of the simple rules on finite graphs under the death-birth updating and the imitation updating discovered by Ohtsuki, Hauert, Lieberman and Nowak [Nature 441 (2006) 502-505]. Each rule specifies a payoff-ratio cutoff point for the magnitude of fixation probabilities of the underlying evolutionary game between cooperators and defectors. We view the Markov chains associated with the two updating mechanisms as voter model perturbations. Then we present a first-order approximation for fixation probabilities of general voter model perturbations on finite graphs subject to small perturbation in terms of the voter model fixation probabilities. In the context of regular graphs, we obtain algebraically explicit first-order approximations for the fixation probabilities of cooperators distributed as certain uniform distributions. These approximations lead to a rigorous proof that both of the rules of Ohtsuki et al. are valid and are sharp.Comment: Published in at http://dx.doi.org/10.1214/12-AAP849 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org