Systemic risk contributions: a credit portfolio approach

We put forward a Merton-type multi-factor portfolio model for assessing banks' contributions to systemic risk. This model accounts for the major drivers of banks' systemic relevance: size, default risk and correlation of banks' assets as a proxy for interconnectedness. We measure systemic risk in terms of the portfolio expected shortfall (ES). Banks' (marginal) risk contributions are calculated based on partial derivatives of the ES in order to ensure a full risk allocation among institutions. We compare the performance of an importance sampling algorithm with a fast analytical approximation of the ES and the marginal risk contributions. Furthermore, we show empirically for a portfolio of large international banks how our approach could be implemented to compute bank-specific capital surcharges for systemic risk or stabilisation fees. We find that size alone is not a reliable proxy for the systemic importance of a bank in this framework. In order to smooth cyclical fluctuations of the risk measure, we explore a time-varying confidence level of the ES. --systemic risk contributions,systemic capital charge,expected shortfall,importance sampling,granularity adjustment

Cross-linguistic patterns in the acquisition of quantifiers.

Learners of most languages are faced with the task of acquiring words to talk about number and quantity. Much is known about the order of acquisition of number words as well as the cognitive and perceptual systems and cultural practices that shape it. Substantially less is known about the acquisition of quantifiers. Here, we consider the extent to which systems and practices that support number word acquisition can be applied to quantifier acquisition and conclude that the two domains are largely distinct in this respect. Consequently, we hypothesize that the acquisition of quantifiers is constrained by a set of factors related to each quantifier's specific meaning. We investigate competence with the expressions for "all," "none," "some," "some…not," and "most" in 31 languages, representing 11 language types, by testing 768 5-y-old children and 536 adults. We found a cross-linguistically similar order of acquisition of quantifiers, explicable in terms of four factors relating to their meaning and use. In addition, exploratory analyses reveal that language- and learner-specific factors, such as negative concord and gender, are significant predictors of variation.This is the author accepted manuscript. The final version is available from the National Academy of Sciences via http://dx.doi.org/10.1073/pnas.160134111

A crosslinguistic study of symmetrical judgments

A longstanding puzzle in developmental linguistics is why children are more permissive than adults in assigning distributive interpretations to sentences with the universal quantifiers each, every, and all under certain experimental conditions. One well-known controversial issue in this area is children’s symmetrical judgments of universally quantified sentences. Symmetrical judgments are elicited when a child is asked to judge if a sentence including a universal quantifier describes a visual context depicting an incomplete distributive relation. The following three judgment types have been included in the set of symmetrical judgment types in the literature (examples from Kang, 2001).peer-reviewe

A hierarchical model of tail dependent asset returns for assessing portfolio credit risk

This paper introduces a multivariate pure-jump Lévy process which allows for skewness and excess kurtosis of single asset returns and for asymptotic tail dependence in the multivariate setting. It is termed Variance Compound Gamma (VCG). The novelty of my approach is that, by applying a two-stage stochastic time change to Brownian motions, I derive a hierarchical structure with different properties of inter- and intra-sector dependence. I investigate the properties of the implied static copula families and come to the conclusion that they are ordered with respect to their parameters and that the lower-tail dependence of the intra-sector copula is increasing in the absolute values of skewness parameters. Furthermore, I show that the joint characteristic function of the VCG asset returns can be explicitly given as a nested Archimedean copula of their marginal characteristic functions. Applied to credit portfolio modelling, the framework introduced results in a more conservative tail risk assessment than a Gaussian framework with the same linear correlation structure, as I show in a simulation study. To foster the simulation efficiency, I provide an Importance Sampling algorithm for the VCG portfolio setting

Systemic Risk Contributions: A Credit Portfolio Approach

We put forward a Merton-type multi-factor portfolio model for assessing banks' contributions to systemic risk. This model accounts for the major drivers of banks' systemic relevance: size, default risk and correlation of banks' assets as a proxy for interconnectedness. We measure systemic risk in terms of the portfolio expected shortfall (ES). Banks' (marginal) risk contributions are calculated based on partial derivatives of the ES in order to ensure a full risk allocation among institutions. We compare the performance of an importance sampling algorithm with a fast analytical approximation of the ES and the marginal risk contributions. Furthermore, we show empirically for a portfolio of large international banks how our approach could be implemented to compute bank-specific capital surcharges for systemic risk or stabilisation fees. We find that size alone is not a reliable proxy for the systemic importance of a bank in this framework. In order to smooth cyclical fluctuations of the risk measure, we explore a time-varying confidence level of the ES

Default dependence among corporate bond issuers: empirical evidence from time series data

This study shows that the extent to which the asset returns of different obligors are correlated is of vital importance for a realistic assessment credit portfolio risk. The high empirical relevance of this phenomenon is demonstrated by applying a likelihood-based estimation procedure to time series data on historical default frequencies. It turns out that, apparently, the default probabilities of speculative-grade debtors are much more highly correlated than the ones of investment-grade borrowers.

Approximate value-at-risk calculation for heterogeneous loan portfolios: Possible enhancements of the Basel II methodology

This paper presents three possible methods by which the credit value at risk estimates coming from the Basel II IRB approach can be significantly improved upon. The feasibility of the suggested approaches is substantiated by applying it to an exemplary model portfolio.Credit value at risk Basel II Moment matching Fourier transform Edgeworth expansion

A Hierarchical Archimedean Copula for Portfolio Credit Risk Modelling

I introduce a novel, hierarchical model of tail dependent asset returns which can be particularly useful for measuring portfolio credit risk within the structural framework. To allow for a stronger dependence within sub-portfolios than between them, I utilise the concept of nested Archimedean copulas, but modify the nesting procedure to ensure the compatibility of copula generators by construction. This makes sampling straightforward. Moreover, I provide details on a particular specification based on a gamma mixture of powers. This model allows for lower tail dependence, resulting in a more conservative credit risk assessment than a comparable Gaussian model. I illustrate the extent of model risk when calculating VaR or Expected Shortfall for a credit portfolio

Operationalising the countercyclical capital buffer: indicator selection, threshold identification and calibration options

This paper presents the analysis underpinning the ESRB Recommendation on guidance on setting countercyclical buffer rates (ESRB 2014/1). The Recommendation is designed to help authorities tasked with setting the countercyclical capital buffer (CCB) to operationalise this new macroprudential instrument. It follows on from the EU prudential rules for the banking system that came into effect on 1 January 2014