Structural credit risk models with subordinated processes

We discuss structural models based on Merton's framework. First, we observe that the classical assumptions of the Merton model are generally rejected. Secondly, we implement a structural credit risk model based on stable non-Gaussian processes as a representative of subordinated models in order to overcome some drawbacks of the Merton one. Finally, following the KMV-Merton estimation methodology, we propose an empirical comparison between the results obtained from the classical KMV-Merton model and the stable Paretian one. In particular, we suggest alternative parameter estimation for subordinated processes, and we optimize the performance for the stable Paretian model.Web of Scienceart. no. 13827

Empirical Implementation of a 2-Factor Structural Model for Loss-Given-Default

In this study we develop a theoretical model for ultimate loss-given default in the Merton (1974) structural credit risk model framework, deriving compound option formulae to model differential seniority of instruments, and incorporating an optimal foreclosure threshold. We consider an extension that allows for an independent recovery rate process, representing undiversifiable recovery risk, having a stochastic drift. The comparative statics of this model are analyzed and compared and in the empirical exercise, we calibrate the models to observed LGDs on bonds and loans having both trading prices at default and at resolution of default, utilizing an extensive sample of losses on defaulted firms (Moody’s Ultimate Recovery Database™), 800 defaults in the period 1987-2008 that are largely representative of the U.S. large corporate loss experience, for which we have the complete capital structures and can track the recoveries on all instruments from the time of default to the time of resolution. We find that parameter estimates vary significantly across recovery segments, that the estimated volatilities of recovery rates and of their drifts are increasing in seniority (bank loans versus bonds). We also find that the component of total recovery volatility attributable to the LGD-side (as opposed to the PD-side) systematic factor is greater for higher ranked instruments and that more senior instruments have lower default risk, higher recovery rate return and volatility, as well as greater correlation between PD and LGD. Analyzing the implications of our model for the quantification of downturn LGD, we find the ratio of the later to ELGD (the “LGD markup”) to be declining in expected LGD, but uniformly higher for lower ranked instruments or for higher PD-LGD correlation. Finally, we validate the model in an out-of-sample bootstrap exercise, comparing it to a high-dimensional regression model and to a non-parametric benchmark based upon the same data, where we find our model to compare favorably. We conclude that our model is worthy of consideration to risk managers, as well as supervisors concerned with advanced IRB under the Basel II capital accord.LGD; credit risk; default; structural model

Collateralised loan obligations (CLOs) : a primer

The following descriptive paper surveys the various types of loan securitisation and provides a working definition of so-called collateralised loan obligations (CLOs). Free of the common rhetoric and slogans, which sometimes substitute for understanding of the complex nature of structured finance, this paper describes the theoretical foundations of this specialised form of loan securitisation. Not only the distinctive properties of CLOs, but also the information economics inherent in the transfer of credit risk will be considered, so that we can equally privilege the critical aspects of security design in the structuring of CLO transactions

Price Discovery of Credit Spreads for Japanese Mega-Banks: Subordinated Bond and CDS

This paper empirically investigates the determinants of credit spreads for Japanese mega-banks with emphasis on comparing subordinated CDS spreads with the subordinated bond spreads from the viewpoint of price discovery in both credit markets. The main findings are summarized as follows. First, subordinated CDS and subordinated bond spreads are significantly cointegrated for most banks, and price discovery measures suggest that the CDS spread plays a more dominant role in price discovery than the bond spread. Second, although both CDS and bond spreads significantly react to the Japanese sovereign CDS spread, only the CDS spread reacts significantly to other financial market variables including its own volatility and equity return. Third, both spreads are responsive to the changes in fundamental accounting variables such as the capital? asset ratio and the nonperforming loan ratio. These accounting variables are likely to constitute common factors that are behind the cointegration relationship. Last, significant volatility spillovers are detected from the CDS to bond spreads. This result implies that new information flows more in this direction.Subordinated Bond, Credit Default Swap, Japanese Banks, Price Discovery, Volatility Spillover, Bivariate GARCH

Rettung durch Regulierung? Eckpunkte des Liikanen-Berichts

This paper summarizes the key proposals of the report by the Liikanen Commission. It starts with an explanation of a crisis narrative underlying the Report and its proposals. The proposals aim for a revitalization of market discipline in financial markets. The two main structural proposals of the Liikanen Report are: first, for large banks, the separation of the trading business from other parts of the banking business (the "Separation Proposal"), and the mandatory issuing of subordinated bank debt thought to be liable (the strict "Bail-in Proposal"). The credibility of this commitment to private liability is achieved by strict holding restrictions. The anticipated consequences of the introduction of these structural regulations for the financial industry and markets are addressed in a concluding part.Ausgehend von einer Erläuterung der Kriseninterpretation (crisis narrative), wie sie in dem Bericht der Liikanen-Kommission zugrunde liegt, werden die nach Ansicht des Verfassers zentralen Vorschläge des Kommissionsberichts ausgewählt, vorgestellt und in den größeren Rahmen einer erneuerten Ordnungspolitik für die Finanzmärkte Europas eingeordnet. Die mit den Vorschlägen eng zusammenhängenden Reformelemente der Bankenunion werden in diesem Text bewusst ausgeklammert. Die beiden zentralen Strukturvorschläge des Liikanen-Berichts betreffen die Abspaltung der Handelsgeschäfte von dem Universalbankengeschäft für große, internationale Banken (der Trennbankenvorschlag), sowie die verpflichtende Emission nachrangigen, glaubwürdig haftenden Fremdkapitals (der strenge Bail-in Vorschlag). Glaubwürdigkeit der Haftungszusage wird durch strenge Halterestriktionen erreicht. Vorhersehbare Folgerungen einer Einführung dieser Strukturregeln für die Finanzindustrie und -märkte werden in einem abschließenden Teil angesprochen

Asset pricing and investor risk in subordinated asset securitisation

As a sign of ambivalence in the regulatory definition of capital adequacy for credit risk and the quest for more efficient refinancing sources collateral loan obligations (CLOs) have become a prominent securitisation mechanism. This paper presents a loss-based asset pricing model for the valuation of constituent tranches within a CLO-style security design. The model specifically examines how tranche subordination translates securitised credit risk into investment risk of issued tranches as beneficial interests on a designated loan pool typically underlying a CLO transaction. We obtain a tranchespecific term structure from an intensity-based simulation of defaults under both robust statistical analysis and extreme value theory (EVT). Loss sharing between issuers and investors according to a simplified subordination mechanism allows issuers to decompose securitised credit risk exposures into a collection of default sensitive debt securities with divergent risk profiles and expected investor returns. Our estimation results suggest a dichotomous effect of loss cascading, with the default term structure of the most junior tranche of CLO transactions (“first loss position”) being distinctly different from that of the remaining, more senior “investor tranches”. The first loss position carries large expected loss (with high investor return) and low leverage, whereas all other tranches mainly suffer from loss volatility (unexpected loss). These findings might explain why issuers retain the most junior tranche as credit enhancement to attenuate asymmetric information between issuers and investors. At the same time, the issuer discretion in the configuration of loss subordination within particular security design might give rise to implicit investment risk in senior tranches in the event of systemic shocks. JEL Classifications: C15, C22, D82, F34, G13, G18, G2

Loss Given Default Modelling: Comparative Analysis

In this study we investigated several most popular Loss Given Default (LGD) models (LSM, Tobit, Three-Tiered Tobit, Beta Regression, Inflated Beta Regression, Censored Gamma Regression) in order to compare their performance. We show that for a given input data set, the quality of the model calibration depends mainly on the proper choice (and availability) of explanatory variables (model factors), but not on the fitting model. Model factors were chosen based on the amplitude of their correlation with historical LGDs of the calibration data set. Numerical values of non-quantitative parameters (industry, ranking, type of collateral) were introduced as their LGD average. We show that different debt instruments depend on different sets of model factors (from three factors for Revolving Credit or for Subordinated Bonds to eight factors for Senior Secured Bonds). Calibration of LGD models using distressed business cycle periods provide better fit than data from total available time span. Calibration algorithms and details of their realization using the R statistical package are presented. We demonstrate how LGD models can be used for stress testing. The results of this study can be of use to risk managers concerned with the Basel accord compliance

Characteristic Function of Time-Inhomogeneous L\'evy-Driven Ornstein-Uhlenbeck Processes

Distributional properties -including Laplace transforms- of integrals of Markov processes received a lot of attention in the literature. In this paper, we complete existing results in several ways. First, we provide the analytical solution to the most general form of Gaussian processes (with non-stationary increments) solving a stochastic differential equation. We further derive the characteristic function of integrals of L\'evy-processes and L\'evy driven Ornstein-Uhlenbeck processes with time-inhomogeneous coefficients based on the characteristic exponent of the corresponding stochastic integral. This yields a two-dimensional integral which can be solved explicitly in a lot of cases. This applies to integrals of compound Poisson processes, whose characteristic function can then be obtained in a much easier way than using joint conditioning on jump times. Closed form expressions are given for gamma-distributed jump sizes as an example.Comment: 15 pages, 26 pages, to appear in Statistics and Probability Letter

Single and joint default in a structural model with purely discontinuous assets

Structural models of credit risk are known to present both vanishing spreads at very short maturities and a poor spread fit over longer maturities. The former shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuous assets. In this paper we resort to a pure jump process of the Variance-Gamma type. First we calibrate the corresponding Merton type structural model to single-name data for the DJ CDX NA IG and CDX NA HY components. By so doing, we show that it circumvents also the diffusive structural models difficulties over longer horizons. In particular, it corrects for underprediction of low risk spreads and overprediction of high risk ones. Then we extend the model to joint default, resorting to a recent formulation of the VG multivariate model and without superimposing a copula choice. We fit default correlation for a sample of CDX NA names, using equity correlation. The main advantage of our joint model with respect to the existing non diffusive ones is that it allows calibration without the equicorrelation assumption, but still in a parsimonious way. As an example of the default assessments which the calibrated model can provide, we price a FtD swap.credit risk, structural models, Lévy asset prices, default probability, joint default.

Statistical Inference for Time-changed Brownian Motion Credit Risk Models

We consider structural credit modeling in the important special case where the log-leverage ratio of the firm is a time-changed Brownian motion (TCBM) with the time-change taken to be an independent increasing process. Following the approach of Black and Cox, one defines the time of default to be the first passage time for the log-leverage ratio to cross the level zero. Rather than adopt the classical notion of first passage, with its associated numerical challenges, we accept an alternative notion applicable for TCBMs called "first passage of the second kind". We demonstrate how statistical inference can be efficiently implemented in this new class of models. This allows us to compare the performance of two versions of TCBMs, the variance gamma (VG) model and the exponential jump model (EXP), to the Black-Cox model. When applied to a 4.5 year long data set of weekly credit default swap (CDS) quotes for Ford Motor Co, the conclusion is that the two TCBM models, with essentially one extra parameter, can significantly outperform the classic Black-Cox model.Comment: 21 pages, 3 figures, 2 table