Spread Curves Research Articles

Currency dependence of corporate credit spreads

Many pricing and risk management models need credit spread curves as an input. In the corporate bond market the estimation of credit spread curves is not trivial. Most issuers have only too few bonds outstanding and frequently these bonds are denominated in different currencies. To ensure a sufficient number of bonds for the estimation procedure in many cases bonds in different currencies have to be used which implies that the estimation procedure has to take into account potential currency effects. Under the hypothesis of zero correlation between the default variables and the exchange rates deflated by the relevant money market accounts we show using a rather general pricing framework that credit spreads are expected to be equal across different currencies. This paper analyses these effects and presents a new model which allows to estimate a credit spread curve for a single issuer with bonds in different currencies. This new model is based on the multi-curve estimation approach which allows a parsimonious joint estimation of a risk free term structure and the credit spread curve of the issuer. We reject the hypothesis of zero correlation between credit and exchange rate risk and present empirical evidence that there are significant differences of issuer specific credit spreads across different currencies in a representative sample of international corporate bonds. Moreover, this implies that dollar related credit spread curves cannot be used without special care for pricing defaultable claims denominated in other currencies.

Implied migration rates from credit barrier models

The risk-neutral credit migration process captures quantitative information which is relevant to the pricing theory and risk management of credit derivatives. In this article, we derive implied migration rates by means of a recently introduced credit barrier model which is calibrated on the basis of aggregate information such as credit migration rates and credit spread curves. The model is characterized by an underlying stochastic process that represents credit quality, and default events are associated to barrier crossings. The stochastic process has state dependent volatility and jumps which are estimated by using empirical migration and default rates. A risk-neutralizing drift and forward liquidity spreads are estimated to consistently match the average spread curves corresponding to all the various ratings. The implied migration rates obtained with our credit barrier model are then compared with those obtained via the Kijima–Komoribayashi model.

Discrete credit barrier models

The model introduced in this article is designed to provide a consistent representation for both the real-world and pricing measures for the credit process. We find that good agreement with historical and market data can be achieved across all credit ratings simultaneously. The model is characterized by an underlying stochastic process that takes on values on a discrete lattice and represents credit quality. Rating transitions are associated with barrier crossings and default events are associated with an absorbing state. The stochastic process has state-dependent volatility and jumps which are estimated by using empirical migration and default rates. A risk-neutralizing drift is estimated to consistently match the average spread curves corresponding to all the various ratings.

A simple model for credit migration and spread curves

We propose and examine a simple model for credit migration and spread curves of a single firm both under real-world and risk-neutral measures. This model is a hybrid of a structural and a reduced-form model. Default is triggered either by successive downgradings of the firm or an unpredictable jump of the state process. The default time is accordingly decomposed into predictable and totally inaccessible part.

The Term Structure of Sovereign Spreads in Emerging Markets

A simple structural model to estimate the term structure of sovereign spreads and the implied default probability of a selected group of emerging countries can account for more than 50% of the J.P. Morgan EMBIG index. The real exchange rate dynamics, modeled as a pure diffusion process, are assumed to trigger default events. Relaxing the hypothesis of market completeness, the model generates sovereign spread curves consistent with market data. The robustness of the model indicates a need to reexamine the criticism that structural models underestimate market spreads. The results suggest that the market tends to overprice the spreads for Brazil by 120 basis points on average, but it reproduces the market behavior for Mexico, Russia, and Turkey. These findings are supported by credit rating agency upgrades of the ratings for Brazil in the second half of 2004, just after the study period.

Parsimonious Estimation of Credit Spreads

The traditional method of credit spread estimation based on subtracting independently estimated risk-free and risky term structures of interest rates can yield unrealistically shaped and often irregular credit spread curves. A more parsimonious joint estimation of the risk-free term structure and the credit spread might serve be a good alternative, but it is hard to decide whether a seemingly irregular shape of the credit spread curve is an economic result or is merely an artifact of the estimation model. An empirical examination of European Monetary Union government bond data shows that traditional estimation models with different functional forms produce differing irregularities in the credit spread curves, while joint estimation procedures result in well-behaved and consistent curves that are less volatile. The more parsimonious joint estimation procedures have virtually the same explanatory power as the traditional methods. A simple linear joint cubic splines specification performs surprisingly well compared to a more comprehensive non-linear model.

The Term Structure of Sovereign Spreads in Emerging Markets: A Calibration Approach for Structural Models

This paper proposes a simple structural model to estimate the term structure of sovereign spreads and the implied default probability of a selected group of emerging countries, which accounts for more than 50% of the J. P. Morgan EMBIG index. The real exchange rate dynamics, modeled as a pure diffusion process, are assumed to trigger default event. By relaxing the hypothesis of market completeness, the calibrated model generates sovereign spread curves consistent with market data, giving average deviations below 30 (Mexico, Russia and Turkey) or 60 (Brazil) basis points over time. We show the robustness of the model and argue that the criticism of structural models for underestimating the magnitude of market spreads should be reconsidered. The results suggest that the market tends to overprice the spreads for Brazil, whereas for Mexico, Russia and Turkey the model reproduces the market behavior.

Currency Dependence of Corporate Credit Spreads

Many pricing and risk management models need credit spread curves as an input. In the corporate bond market the estimation of credit spread curves is not trivial. Most issuers have only too few bonds outstanding and frequently these bonds are denominated in different currencies. To ensure a sufficient number of bonds for the estimation procedure in many cases bonds in different currencies have to be used which implies that the estimation procedure has to take into account potential currency effects. Under the hypothesis of zero correlation between the default variables and the exchange rates deflated by the relevant money market accounts we show using a rather general pricing framework that credit spreads are expected to be equal across different currencies. This paper analyses these effects and presents a new model which allows to estimate a credit spread curve for a single issuer with bonds in different currencies. This new model is based on the multi-curve estimation approach which allows a parsimonious joint estimation of a risk free term structure and the credit spread curve of the issuer. We reject the hypothesis of zero correlation between credit and exchange rate risk and present empirical evidence that there are significant differences of issuer specific credit spreads across different currencies in a representative sample of international corporate bonds. Moreover, this implies that dollar related credit spread curves cannot be used without special care for pricing defaultable claims denominated in other currencies.

Valuation of Sovereign Debt with Strategic Defaulting and Rescheduling

This paper provides a simple model of the rescheduling of debt following a sovereign default as a bond exchange. In case of default, the sovereign offers a new bond with lower coupon and principal. The debtors accept the offer if the value of the new bonds is higher than the proceedings of the litigation of the sovereign. Both the default decision of the sovereign as well as the exchange offer are modeled endogenously and in closed form. The resulting formulas for bond value and credit spreads are in closed form as well. The analysis yields credit spread curves similar to corporate credit curves: For high risk issuers, i.e., sovereign with low country wealth relative to debt level, and high litigation costs, the credit spread curves are hump-shaped. Better quality issues exhibit increasing credit spread curves. The numerical analysis with reasonable parameters yields credit spreads of a size compatible to market spreads. A comparison to corporate debt supports the stylized fact that, using the same parameters, corporate debt is less risky than sovereign debt since the threat of liquidation is stronger than the threat of litigation.

Parsimonious Estimation of Credit Spreads

The traditional method of credit spread estimation is based on subtracting independently estimated risk-free and risky term structures of interest rates which in many cases yields unrealistically shaped and often irregular credit spread curves. A parsimonious joint estimation of the risk-free term structure and the credit spread as proposed by Houweling et al. (2001) might serve as a valuable alternative to overcome this drawback but it is hard to decide whether a seemingly irregular shape of the credit spread curve is economically caused by the data or is only an artefact of the functional form of the estimation model. Results of an empirical examination of EMU government bond data show that traditional estimation models with different functional forms yield differing irregularities in the credit spread curves whereas joint estimation procedures result in well-behaving and coinciding curves. Moreover, the explanatory power of the more parsimonious joint estimation procedures is virtually equal to the traditional methods. This is strong evidence for the superiority of a joint estimation procedure of credit spread curves. Finally, we conclude that a simple linear joint cubic splines specification performs surprisingly well compared to a numerically more affording non-linear model.

The Corporate Spread Curve and Industrial Production in the United States

The term structure of domestic investment grade bond spreads - or corporate spread curve - contains useful information to predict future changes in industrial production, beyond the information already contained in interest rates, commercial paper-treasury bill spreads, and lagged values of industrial production. In fact, the corporate spread curve can explain the cumulative growth rate of industrial production over 3- to 48-month horizons, and the marginal growth rate over 6- to 18-month horizons. Unlike other financial variables, the corporate spread curve has been a stable predictor of real activity for the last fifteen years.

The Corporate Spread Curve and Industrial Production in the United States

The term structure of domestic investment grade bond spreads - or corporate spread curve - contains useful information to predict future changes in industrial production, beyond the information already contained in interest rates, commercial paper-treasury bill spreads, and lagged values of industrial production. In fact, the corporate spread curve can explain the cumulative growth rate of industrial production over 3- to 48-month horizons, and the marginal growth rate over 6- to 18-month horizons, Unlike other financial variables, the corporate spread curve has been a stable predictor of real activity for the last fifteen years.

The term structure of credit spreads with jump risk

Default risk analysis is important for valuing corporate bonds, swaps, and credit derivatives and plays a critical role in managing the credit risk of bank loan portfolios. This paper offers a theory to explain the observed empirical regularities on default probabilities, recovery rates, and credit spreads. It incorporates jump risk into the default process. With the jump risk, a firm can default instantaneously because of a sudden drop in its value. As a result, a credit model with the jump risk is able to match the size of credit spreads on corporate bonds and can generate various shapes of yield spread curves and marginal default rate curves, including upward-sloping, downward-sloping, flat, and hump-shaped, even if the firm is currently in a good financial standing. The model also links recovery rates to the firm value at default so that the variation in recovery rates is endogenously generated and the correlation between recovery rates and credit ratings before default reported in Altman [J. Finance 44 (1989) 909] can be justified.

The joint estimation of term structures and credit spreads

We present a new framework for the joint estimation of the default-free government term structure and corporate credit spread curves. By using a data set of liquid, German mark denominated bonds, we show that this yields more realistic spreads than traditionally obtained spread curves that result from subtracting independently estimated government and corporate term structures. The obtained spread curves are smooth functions of time to maturity, as opposed to the twisting curves one gets from the traditional method, and are less sensitive to model specifications. To determine the ‘optimal’ model specification, we use a newly developed test statistic that compares spread curves from competing models.

A simulation environment for discontinuous portfolio value processes

AbstractWe present a simulation‐based approach to the estimation of portfolio's Value‐at‐Risk – VaR—, based on the definition of a jump‐diffusion continuous time process driven by Wiener and Poisson uncertainty. We introduce to this end a novel characterization of the intensity rate of the Poisson process, modelling the arrival of shocks to the market, as a function of a credit spread curve estimated in high‐risk emerging bond markets. The procedure is described and tested on the August 1998 Russian crisis whose impact on liquid equity markets is also estimated. Copyright © 2001 John Wiley & Sons, Ltd.

Credit Spread Bounds and their Implications for Credit Risk Modeling

A basic requirement for a credit risk model is that it should not imply negative default probabilities. In this paper, we explore the implications of this condition for credit risk modeling. More specifically, we use the condition as a diagnostic tool to investigate if a particular model is consistent with a given set of credit spreads. We show that under this condition, each model has two credit spread boundaries which can be calculated analytically, and the model is correctly specified if and only if the observed credit spread curve lies within the two boundaries. These analytical formulas for the boundaries also allow us to derive some general properties of a large class of credit risk models. Our study also adds to the literature on pricing defaultable claims off the default probability curve, a method widely used in practice. It is well-known that negative default probabilities frequently occur in constructions of default probability curves. Our analysis provides one possible explanation of why this problem happens and also suggests how the problem may be solved (or at least alleviated).

Credit Spread Curves and Credit Ratings

Credit Spread Curves and Credit Ratings

The Joint Estimation of Term Structures and Credit Spreads

We present a new framework for the joint estimation of the default-free term structure of interest rates and corporate credit spread curves. It specifies the discount curve of a specific credit rating class as the sum of the government discount function and a discount spread function. Both functions are modelled using splines so that we can jointly estimate the default-free government term structure and corporate credit spread curves with least squares. We construct confidence intervals around the estimated term structures and credit spreads and use them to determine the number of knots and the order of the involved spline functions. By using a high-quality data set of German mark denominated bonds, we show that the new framework yields more realistic spreads than conventionally obtained spread curves that result from subtracting independently estimated government and corporate term structures. The estimated spread curves are now smooth functions of time to maturity, as opposed to the twisting curves one gets from the traditional method, and are less sensitive to model specifications. Moreover, the implied corporate term structures have tighter confidence bands. The credit spreads and term structures that result from the framework are therefore more suited to be used as input to, e.g., models that asses the credit risk in derivatives, pricing models for credit derivatives and corporate bonds, risk management procedures, and time series analyses of credit spreads.

A Jump-Diffusion Approach to Modeling Credit Risk and Valuing Defaultable Securities

The existing structural models of credit risk have relied almost exclusively on diffusion processes to model the evolution of firm value. While a diffusion approach is convenient, it has produced very disappointing results in empirical application. Jones, Mason, and Rosenfeld (1984) find that the credit spreads on corporate bonds are too high to be matched by the diffusion approach. Also, because the instantaneous default probability of a healthy firm is zero under a continuous process, the diffusion approach predicts that the term structure of credit spreads should always start at zero and slope upward for firms that are not currently in financial distress. Empirical literature shows, however, that the actual credit spread curves are sometimes flat or even downward-sloping. If a diffusion approach cannot capture the basic features of credit risk, what approach can? This paper develops a new structural approach to valuing default-risky securities by modeling the evolution of firm value as a jump-diffusion process. Under a jump-diffusion process, a firm can default instantaneously because of a sudden drop in its value. With this characteristic, a jump-diffusion model can match the size of credit spreads on corporate bonds and can generate various shapes of yield spread curves and marginal default rate curves. The model also links recovery rates to firm value at default in a natural way so that variation in recovery rates is endogenously generated in the model. The model is also consistent with many other stylized empirical facts in the credit-risk literature.

A Jump-Diffusion Approach to Modeling Credit Risk and Valuing Defaultable Securities

The existing structural models of credit risk have relied almost exclusively on diffusion processes to model the evolution of firm value. While a diffusion approach is convenient, it has produced very disappointing results in empirical application. Jones, Mason, and Rosenfeld (1984) find that the credit spreads on corporate bonds are too high to be matched by the diffusion approach. Also, because the instantaneous default probability of a healthy firm is zero under a continuous process, the diffusion approach predicts that the term structure of credit spreads should always start at zero and slope upward for firms that are not currently in financial distress. Empirical literature shows, however, that the actual credit spread curves are sometimes flat or even downward-sloping. If a diffusion approach cannot capture the basic features of credit risk, what approach can? This paper develops a new structural approach to valuing default-risky securities by modeling the evolution of firm value as a jump-diffusion process. Under a jump-diffusion process, a firm can default instantaneously because of a sudden drop in its value. With this characteristic, a jump-diffusion model can match the size of credit spreads on corporate bonds and can generate various shapes of yield spread curves and marginal default rate curves. The model also links recovery rates to firm value at default in a natural way so that variation in recovery rates is endogenously generated in the model. The model is also consistent with many other stylized empirical facts in the credit-risk literature.