Abstract not found

This paper develops a method for statistical estimation of the dependence structure of financial assets. As we are interested mainly in applications to credit risk, our approach focuses directly on the copula function of a random vector and works independently of any marginal assumptions. We use the class of elliptical copulas, which provide a natural extension to the standard for the practice Gaussian copula and a flexible model for joint extreme events. We calibrate the linear correlation coe#cients using the whole sample of observations and the non-linear (tail) dependence coe#cients using only the extreme observations. We provide theoretical as well as numerical support for our method.

This paper investigates the pricing of step-up bonds, ie, corporate bonds with provisions stating that the coupon payments increase as the credit rating level of the issuer declines. To assess the risk-neutral rating transition probabilities necessary to price these bonds, we introduce a new calibration method within the reduced-form rating-based model of Jarrow, Lando and Turnbull (1997). We also treat split ratings and adjust for rating outlook. Step-up bonds have been issued in large quantities in the European telecom sector, and we find that, through most of the sample, step-up bonds issued by the two largest issuers have traded at a discount relative to comparable fixed-coupon bonds from the same issuers. Our findings cannot be attributed to traditional liquidity factors, and they suggest that issuing step-up bonds increased the cost of capital for the issuers.

We consider a portfolio credit risk model in the spirit of CreditMetrics [15]. The multivariate normally distributed underlying risk factors in that model are replaced by more general multivariate elliptical factors with heavy-tailed marginals, intro-ducing tail-dependence. We consider a full-scale version of the model, i.e. we incor-porate not only the default risk, but also rating migrations, credit spread volatility and recovery risk. We derive an upper bound of the portfolio loss distribution, which is particularly accurate at high loss levels. Given the complexity of our model, we obtain this results using a mixture of analytic techniques and Monte Carlo simulation. We conclude with an approximation of VaR and a new method to determine the contributions of the individual credits to the overall portfolio risk.

at discrete time points

In theory the potential for credit risk diversification for banks could be substantial. Portfolios are large enough that idiosyncratic risk is diversified away leaving exposure to systematic risk. The potential for portfolio diversification is driven broadly by two characteristics: the degree to which systematic risk factors are correlated with each other and the degree of dependence individual firms have to the di¤erent types of risk factors. We propose a model for exploring these dimensions of credit risk diversification: across industry sectors and across different countries or regions. We find that full firm-level parameter heterogeneity matters a great deal for capturing di¤erences in simulated credit loss distributions. Imposing homogeneity results in overly skewed and fat-tailed loss distributions. These differences become more pronounced in the presence of systematic risk factor shocks: increased parameter heterogeneity greatly reduces shock sensitivity. Allowing for regional parameter heterogeneity seems to better approximate the loss distributions generated by the fully heterogeneous model than allowing just for industry heterogeneity. The regional model also exhibits less shock sensitivity.

Abstract not found

Abstract 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 model of friction the migration policy is modelled in terms of thresholds which have to be crossed by default probability estimates before an up- or downgrade occurs. Default probability estimates have to change by around two notches before the rating agency reacts. The timeliness differs across the rating spectrum and over the years. During periods with high defaults and for low credit quality firms agencies tend to rate more timely.

This paper assesses whether ratings or market-based credit risk measures are more suitable for formulating portfolio governance rules. Such rules, which consist of buy and sell restrictions, are commonly used in investment management. Based on data from 1983 to 2002, it is not evident that one of the two measures is superior. The relative power of the two measures in predicting defaults depend on the investor’s investment horizon and risk appetite. The results support the agencies ' claim that their policy of reducing rating volatility, which builds on the though-the-cycle approach and the avoidance of frequent rating reversals, is beneficial to bond investors. The results also suggest that widely used statistical measures of rating quality may be insufficient to judge the economic value of rating information in specific contexts.

paper- including earlier versions entitled “A model for corporate bonds, swaps and Treasury securities ” and “A model of swap spreads and corporate bond yields ”- was presented at the BIS workshop on “The Pricing of Credit Risk”, the inaugural WBS fixed income conference in Prague, a meeting of the Moody’s