On singularity formation in three-dimensional vortex sheet evolution

It is shown that if a doubly-infinite vortex sheet has cylindrical shape and strength distributions at some initial time, then this property is retained in its subsequent evolution. It is also shown that in planes normal to the generator of the cylindrical sheet geometry, the nonlinear evolution of the sheet is the same as that of an equivalent strictly two-dimensional sheet motion. These properties are used to show that when an initially flat vortex sheet is subject to a finite-amplitude, three-dimensional normal mode perturbation, weak singularities develop along lines which are oblique to the undisturbed velocity jump vector at a time that can be inferred from an extension of Moore's [Proc. R. Soc. A 365, 105 (1979)] result for two-dimensional motion

Metric Perturbation Approach to Gravitational Waves in Isotropic Cosmologies

Gravitational waves in isotropic cosmologies were recently studied using the gauge-invariant approach of Ellis-Bruni. We now construct the linearised metric perturbations of the background Robertson-Walker space-time which reproduce the results obtained in that study. The analysis carried out here also facilitates an easy comparison with Bardeen.Comment: 29 pages, Latex file, accepted for publication in Physical Review

The Link between Default and Recovery Rates: Theory, Empirical Evidence and Implications

This paper analyzes the association between aggregate default and recovery rates on credit assets, and seeks to empirically explain this critical relationship. We examine recovery rates on corporate bond defaults, over the period 1982-2002. Our econometric univariate and multivariate models explain a significant portion of the variance in bond recovery rates aggregated across all seniority and collateral levels. The central thesis is that aggregate recovery rates are basically a function of supply and demand for the securities, with default rates playing a pivotal role. Such a link would bring about a significant increase in both expected and unexpected losses as measured by some widespread credit risk models, and would affect the procyclicality effects of the New Basel Capital Accord. Our results have also important implications for investors in corporate bonds and bank loans, and for all markets (e.g., securitizations, credit derivatives, etc.) which depend on recovery rates as a key variable

The Link between Default and Recovery Rates

This paper analyzes the association between aggregate default and recovery rates on credit assets, and seeks to empirically explain this critical relationship. We examine recovery rates on corporate bond defaults, over the period 1982-2002. Our econometric univariate and multivariate models explain a significant portion of the variance in bond recovery rates aggregated across all seniority and collateral levels. The central thesis is that aggregate recovery rates are basically a function of supply and demand for the securities, with default rates playing a pivotal role. Such a link would bring about a significant increase in both expected and unexpected losses as measured by some widespread credit risk models, and would affect the procyclicality effects of the New Basel Capital Accord. Our results have also important implications for investors in corporate bonds and bank loans, and for all markets (e.g., securitizations, credit derivatives) that depend on recovery rates as a key variable

The Link between Default and Recovery Rates: Implications for Credit Risk Models and Procyclicality

This paper analyzes the impact of various assumptions about the association between aggregate default probabilities and the loss given default on bank loans and corporate bonds, and seeks to empirically explain this critical relationship. Moreover, it simulates the effects on mandatory capital requirements like those proposed in 2001 by the Basel Committee on Banking Supervision. We present the analysis and results in four distinct sections. The first section examines the literature of the last three decades of the various structural-form, closed-form and other credit risk and portfolio credit value-at-risk (VaR) models and the way they explicitly or implicitly treat the recovery rate variable. Section 2 presents simulation results under three different recovery rate scenarios and examines the impact of these scenarios on the resulting risk measures: our results show a significant increase in both expected and unexpected losses when recovery rates are stochastic and negatively correlated with default probabilities. In Section 3, we empirically examine the recovery rates on corporate bond defaults, over the period 1982-2000. We attempt to explain recovery rates by specifying a rather straightforward statistical least squares regression model. The central thesis is that aggregate recovery rates are basically a function of supply and demand for the securities. Our econometric univariate and multivariate time series models explain a significant portion of the variance in bond recovery rates aggregated across all seniority and collateral levels. Finally, in Section 4 we analyze how the link between default probability and recovery risk would affect the procyclicality effects of the New Basel Capital Accord, due to be released in 2002. We see that, if banks use their own estimates of LGD (as in the “advanced” IRB approach), an increase in the sensitivity of banks’ LGD due to the variation in PD over economic cycles is likely to follow. Our results have important implications for just about all portfolio credit risk models, for markets which depend on recovery rates as a key variable (e.g., securitizations, credit derivatives, etc.), for the current debate on the revised BIS guidelines for capital requirements on bank credit assets, and for investors in corporate bonds of all credit qualities

The Link between Default and Recovery Rates: Implications for Credit Risk Models and Procyclicality

This paper analyzes the impact of various assumptions about the association between aggregate default probabilities and the loss given default on bank loans and corporate bonds, and seeks to empirically explain this critical relationship. Moreover, it simulates the effects on mandatory capital requirements like those proposed in 2001 by the Basel Committee on Banking Supervision. We present the analysis and results in four distinct sections. The first section examines the literature of the last three decades of the various structural-form, closed-form and other credit risk and portfolio credit value-at-risk (VaR) models and the way they explicitly or implicitly treat the recovery rate variable. Section 2 presents simulation results under three different recovery rate scenarios and examines the impact of these scenarios on the resulting risk measures: our results show a significant increase in both expected and unexpected losses when recovery rates are stochastic and negatively correlated with default probabilities. In Section 3, we empirically examine the recovery rates on corporate bond defaults, over the period 1982-2000. We attempt to explain recovery rates by specifying a rather straightforward statistical least squares regression model. The central thesis is that aggregate recovery rates are basically a function of supply and demand for the securities. Our econometric univariate and multivariate time series models explain a significant portion of the variance in bond recovery rates aggregated across all seniority and collateral levels. Finally, in Section 4 we analyze how the link between default probability and recovery risk would affect the procyclicality effects of the New Basel Capital Accord, due to be released in 2002. We see that, if banks use their own estimates of LGD (as in the “advanced” IRB approach), an increase in the sensitivity of banks’ LGD due to the variation in PD over economic cycles is likely to follow. Our results have important implications for just about all portfolio credit risk models, for markets which depend on recovery rates as a key variable (e.g., securitizations, credit derivatives, etc.), for the current debate on the revised BIS guidelines for capital requirements on bank credit assets, and for investors in corporate bonds of all credit qualities

Gauge symmetry breaking on orbifolds

We discuss a new method for gauge symmetry breaking in theories with one extra dimension compactified on the orbifold S^1/Z_2. If we assume that fields and their derivatives can jump at the orbifold fixed points, we can implement a generalized Scherk-Schwarz mechanism that breaks the gauge symmetry. We show that our model with discontinuous fields is equivalent to another with continuous but non periodic fields; in our scheme localized lagrangian terms for bulk fields appear.Comment: 6 pages, 2 figures. Talk given at the XXXVIIth Rencontres de Moriond, "Electroweak interactions and unified theories", Les Arcs, France, 9-16 Mar 2002. Minor changes, one reference adde

Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well defined and bounded. We show that the quantum JSD (QJSD) shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.Comment: 14 pages, corrected equation 1