Capturing Model Risk and Rating Momentum in the Estimation of Probabilities of Default and Credit Rating Migrations

We present two methodologies on the estimation of rating transition probabilities within Markov and non-Markov frameworks. We first estimate a continuous-time Markov chain using discrete (missing) data and derive a simpler expression for the Fisher information matrix, reducing the computational time needed for the Wald confidence interval by a factor of a half. We provide an efficient procedure for transferring such uncertainties from the generator matrix of the Markov chain to the corresponding rating migration probabilities and, crucially, default probabilities. For our second contribution, we assume access to the full (continuous) data set and propose a tractable and parsimonious self-exciting marked point processes model able to capture the non-Markovian effect of rating momentum. Compared to the Markov model, the non-Markov model yields higher probabilities of default in the investment grades, but also lower default probabilities in some speculative grades. Both findings agree with empirical observations and have clear practical implications. We illustrate all methods using data from Moody's proprietary corporate credit ratings data set. Implementations are available in the R package ctmcd.Comment: 22 pages, 5 Figures, 4 Tables. To Appear in Quantitative Financ

Evolutionary estimation of a Coupled Markov Chain credit risk model

There exists a range of different models for estimating and simulating credit risk transitions to optimally manage credit risk portfolios and products. In this chapter we present a Coupled Markov Chain approach to model rating transitions and thereby default probabilities of companies. As the likelihood of the model turns out to be a non-convex function of the parameters to be estimated, we apply heuristics to find the ML estimators. To this extent, we outline the model and its likelihood function, and present both a Particle Swarm Optimization algorithm, as well as an Evolutionary Optimization algorithm to maximize the likelihood function. Numerical results are shown which suggest a further application of evolutionary optimization techniques for credit risk management

Association of HLA types A1-B8-DR3 and B27 with rapid and slow progression of HIV disease

We examined how HLA types A1-B8-DR3 and B27 were related to progression of clinical disease and rate of loss of CD4 lymphocytes in the Edinburgh City Hospital cohort of HIV-positive patients, mainly injection drug users. Patients (n = 692) were prospectively followed from 1985 through March 1994. Accurately estimated seroconversion times were determined retrospectively for a subgroup of 313 (45%). Of 262 patients (39%) who were fully or partially HLA typed, 155 (50%) had known seroconversions. Of 34 patients typed positive for A1-B8-DR3, 29 progressed to CDC stage IV, 22 to AIDS and 20 died. Twelve patients were typed positive for B27; six of these progressed to CDC stage IV, one to AIDS and none died. In a proportional hazards analysis of the 313 patients with known seroconversions, A1-B8-DR3 was significantly associated with covariate-adjusted relative risks of 3.7 (95% CI 1.9-7.2), 3.1 (1.6-6.0) and 1.9 (1.1-3.2) for progression from seroconversion to death, AIDS and CDC stage IV, respectively. Events for B27 were too rare to include B27 in analyses to death and AIDS, but B27 was significantly associated with slower progression to CDC stage IV (0.3, CI 0.1-0.9). Random effects growth curve models were used to estimate individual rates of loss of square root CD4 count and loss of CD4 percentage, for 603 and 617 patients, respectively. A1-B8-DR3 was associated with rapid loss of both markers (p=0.02 and p = 0.01, respectively); B27 was associated with slow loss of both markers (p=0.04 and p<0.005

Factor copula models for item response data

Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses. The factor copula models have interpretations of latent maxima/minima (in comparison with latent means) and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets, and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data

The outer halos of elliptical galaxies

Recent progress is summarized on the determination of the density distributions of stars and dark matter, stellar kinematics, and stellar population properties, in the extended, low surface brightness halo regions of elliptical galaxies. With integral field absorption spectroscopy and with planetary nebulae as tracers, velocity dispersion and rotation profiles have been followed to ~4 and ~5-8 effective radii, respectively, and in M87 to the outer edge at ~150 kpc. The results are generally consistent with the known dichotomy of elliptical galaxy types, but some galaxies show more complex rotation profiles in their halos and there is a higher incidence of misalignments, indicating triaxiality. Dynamical models have shown a range of slopes for the total mass profiles, and that the inner dark matter densities in ellipticals are higher than in spiral galaxies, indicating earlier assembly redshifts. Analysis of the hot X-ray emitting gas in X-ray bright ellipticals and comparison with dynamical mass determinations indicates that non-thermal components to the pressure may be important in the inner ~10 kpc, and that the properties of these systems are closely related to their group environments. First results on the outer halo stellar population properties do not yet give a clear picture. In the halo of one bright galaxy, lower [alpha/Fe] abundances indicate longer star formation histories pointing towards late accretion of the halo. This is consistent with independent evidence for on-going accretion, and suggests a connection to the observed size evolution of elliptical galaxies with redshift.Comment: 8 pages. Invited review to appear in the proceedings of "Galaxies and their Masks" eds. Block, D.L., Freeman, K.C. & Puerari, I., 2010, Springer (New York

Search for the glueball candidates f0(1500) and fJ(1710) in gamma gamma collisions

Data taken with the ALEPH detector at LEP1 have been used to search for gamma gamma production of the glueball candidates f0(1500) and fJ(1710) via their decay to pi+pi-. No signal is observed and upper limits to the product of gamma gamma width and pi+pi- branching ratio of the f0(1500) and the fJ(1710) have been measured to be Gamma_(gamma gamma -> f0(1500)). BR(f0(1500)->pi+pi-) < 0.31 keV and Gamma_(gamma gamma -> fJ(1710)). BR(fJ(1710)->pi+pi-) < 0.55 keV at 95% confidence level.Comment: 10 pages, 3 figure

The effect of asymmetries on stock index return value-at-risk estimates

It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value-at-risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models

Search for supersymmetry with a dominant R-parity violating LQDbar couplings in e+e- collisions at centre-of-mass energies of 130GeV to 172 GeV

A search for pair-production of supersymmetric particles under the assumption that R-parity is violated via a dominant LQDbar coupling has been performed using the data collected by ALEPH at centre-of-mass energies of 130-172 GeV. The observed candidate events in the data are in agreement with the Standard Model expectation. This result is translated into lower limits on the masses of charginos, neutralinos, sleptons, sneutrinos and squarks. For instance, for m_0=500 GeV/c^2 and tan(beta)=sqrt(2) charginos with masses smaller than 81 GeV/c^2 and neutralinos with masses smaller than 29 GeV/c^2 are excluded at the 95% confidence level for any generation structure of the LQDbar coupling.Comment: 32 pages, 30 figure

Search for Bs0B^{0}_{s} oscillations using inclusive lepton events

A search for Bs oscillations is performed using a sample of semileptonic b-hadron decays collected by the ALEPH experiment during 1991-1995. Compared to previous inclusive lepton analyses, the prop er time resolution and b-flavour mistag rate are significantly improved. Additional sensitivity to Bs mixing is obtained by identifying subsamples of events having a Bs purity which is higher than the average for the whole data sample. Unbinned maximum likelihood amplitude fits are performed to derive a lower limit of Dms>9.5 ps-1 at 95% CL. Combining with the ALEPH Ds based analyses yields Dms>9.6 ps-1 at 95% CL.A search for B0s oscillations is performed using a sample of semileptonic b-hadron decays collected by the ALEPH experiment during 1991-1995. Compared to previous inclusive lepton analyses, the proper time resolution and b-flavour mistag rate are significantly improved. Additional sensitivity to B0s mixing is obtained by identifying subsamples of events having a B0s purity which is higher than the average for the whole data sample. Unbinned maximum likelihood amplitude fits are performed to derive a lower limit of Deltam_s>9.5ps^-1 at 95% CL. Combining with the ALEPH D-s based analyses yields Deltam_s>9.6ps^-1 at 95% CL