Limited arbitrage between equity and credit markets

We document that short-horizon pricing discrepancies across firms' equity and credit markets are common and that an economically significant proportion of these are anomalous, indicating a lack of integration between the two markets. Proposing a statistical measure of market integration, we investigate whether equity–credit market integration is related to impediments to arbitrage. We find that time variation in integration across a firm's equity and credit markets is related to firm-specific impediments to arbitrage such as liquidity in equity and credit markets and idiosyncratic risk. Our evidence provides a potential resolution to the puzzle of why Merton model hedge ratios match empirically observed stock-bond elasticities (Schaefer and Strebulaev, 2008) and yet the model is limited in its ability to explain the integration between equity and credit markets (Collin-Dufresne, Goldstein, and Martin, 2001).     

On the calibration of structural credit spread models

Empirical findings are mixed about the performance of structural models for term structure of credit spreads. It is commonly believed that all structural models have equally poor performance after calibration. However, proper calibration is not a trivial issue, especially for highly structural models. This paper proposes a more accurate procedure for calibrating two models: Leland–Toft (J Finance 51:987–1019, 1996) and Collin-Dufresne and Goldstein (J Finance 56:2177–2208, 2001). Using rating-based bond data, we find that the Leland–Toft model has significantly greater explanatory power for credit spreads across rating categories than previously reported. We provide theoretical explanations for these findings, and further extend our empirical analysis to include 286 individual senior bonds. Our findings help clarify the controversies over the performance of structural models in general and that of the Leland–Toft model in particular. In addition, we offer a rigorous procedure that can be used for calibrating other structural models more effectively.      

Leverage, options liabilities, and corporate bond pricing

The two major problems with typical structural models are the failure to attain a positive credit spread in the very short term, and overestimation of the overall level of the credit spread. We recognize the presence of option liabilities in a firm’s capital structure and the effect they have on the firm’s credit spread. Including option liabilities and employing a regime switching interest rate process to capture the business cycle resolves the above-mentioned drawbacks in explaining credit spreads. We find that the credit spread overestimation problem in one of the structural models, Collin-Dufresne and Goldstein (J Finan 56:1929–1957, 2001), can be resolved by combining option liabilities and the regime-switching interest rate process when dealing with an investment grade bond, whereas with junk bonds, only the regime-switching interest rate process is needed. We also examine vulnerable option values, debt values, and zero-coupon bond values with different model settings and leverage ratios.      

Corporate yield spreads and real interest rates

The effect of inflation on the credit spreads of corporate bonds is investigated utilising real instead of nominal interest rates in extensions of the models proposed by Longstaff and Schwartz (1995) and Collin-Dufresne et al. (2001). Inflation is a critical, non-default, component incorporated in nominal bond yields, whose effect has not been considered by existing credit spread theory. In this sense the only true test of models of credit spread pricing must utilise real rates. To illustrate these requirements the Canadian bond data of Jacoby, Liao, and Batten (2009) is utilised. This Canadian data accommodates callability and the tax effects otherwise present in U.S. bond markets. The relation with historical default rates of both U.S. and Canadian bonds is also investigated since this approach is clean of both callability and tax effects. Overall, the analysis provides additional insights into the theoretical drivers of credit spreads as well as helping to explain observed corporate bond yield behaviour in financial markets.     

Expected Default Probabilities in Structural Models: Empirical Evidence

We apply a set of structural models (Black and Cox 1976; Collin-Dufresne and Goldstein 2001; Ericsson and Reneby 1998; Leland and Toft 1996; Longstaff and Schwartz 1995; Merton 1974) to estimate expected default probabilities (EDPs) for a sample of failed and non-failed UK real estate companies. Results are generally consistent with models’ predictions and estimates of EDPs for different models are closely clustered. The results of z-scores and synthetic ratings misclassify 33% of the total sample in contrast to 8% misclassification by structural models. Further analysis of EDPs based on logistic regressions suggests the observed misclassification of the companies by structural models is due to special company management and/or regulatory circumstances rather than limitations of these models.      

Structural Models of Corporate Bond Pricing: An Empirical Analysis

This article empirically tests five structural models of corporatebond pricing: those of Merton (1974), Geske (1977), Longstaffand Schwartz (1995), Leland and Toft (1996), and Collin-Dufresneand Goldstein (2001). We implement the models using a sampleof 182 bond prices from firms with simple capital structuresduring the period 1986–1997. The conventional wisdom isthat structural models do not generate spreads as high as thoseseen in the bond market, and true to expectations, we find thatthe predicted spreads in our implementation of the Merton modelare too low. However, most of the other structural models predictspreads that are too high on average. Nevertheless, accuracyis a problem, as the newer models tend to severely overstatethe credit risk of firms with high leverage or volatility andyet suffer from a spread underprediction problem with saferbonds. The Leland and Toft model is an exception in that itoverpredicts spreads on most bonds, particularly those withhigh coupons. More accurate structural models must avoid featuresthat increase the credit risk on the riskier bonds while scarcelyaffecting the spreads of the safest bonds.     

Identifying Term Structure Volatility from the LIBOR-Swap Curve

This paper proposes a new family of specification tests andapplies them to affine term structure models of the London InterbankOffered Rate (LIBOR)-swap curve. Contrary to Dai and Singleton(2000), the tests show that when standard estimation techniquesare used, affine models do a poor job of forecasting volatilityat the short end of the term structure. Improving the volatilityforecast does not require different models; rather, it requiresa different estimation technique. The paper distinguishes betweentwo econometric procedures for identifying volatility. The "cross-sectional"approach backs out volatility from a cross section of bond yields,and the "time-series" approach imputes volatility from time-seriesvariation in yields. For an affine model, the volatility impliedby the time-series procedure passes the specification tests,while the cross-sectionally identified volatility does not.This is surprising, since under correct specification, the "cross-sectional"approach is maximum likelihood. One explanation is that affinemodels are slightly misspecified; another is that bond yieldsdo not span volatility, as in Collin-Dufresne and Goldstein(2002).     

A bridge from ruin theory to credit risk

The structural model uses the firm-value process and the default threshold to obtain the implied credit spread. Merton’s (J Finance 29:449–470, 1974) credit spread is reported too small compared to the observed market spread. Zhou (J Bank Finance 25:2015–2040, 2001) proposes a jump-diffusion firm-value process and obtains a credit spread that is closer to the observed market spread. Going in a different direction, the reduced-form model uses the observed market credit spread to obtain the probability of default and the mean recovery rate. We use a jump-diffusion firm-value process and the observed credit spread to obtain the implied jump distribution. Therefore, the discrepancy in credit spreads between the structural model and the reduced-form model can be removed. From the market credit spread, we obtain the implied probability of default and the mean recovery rate. When the solvency-ratio process in credit risk and the surplus process in ruin theory both follow jump-diffusion processes, we show a bridge between ruin theory and credit risk so that results developed in ruin theory can be used to develop analogous results in credit risk. Specifically, when the jump is Logexponentially distributed, it results in a Beta distributed recovery rate that is close to market experience. For bonds of multiple seniorities, we obtain closed-form solutions of the mean and variance of the recovery rate. We prove that the defective renewal equation still holds, even if the jumps are possibly negative. Therefore, we can use ruin theory as a methodology for assessing credit ratings.      

The Credit Risk and Pricing of OTC Options

In the over-the-counter (OTC) markets, the options traded are always subject to credit risk. Therefore the counterparty’s credit risk is a striking factor when pricing options, whereas it is not considered in the classic Black-Scholes models. Based on the first passage time models, this paper develops the credit risk and valuation model for the European options in the OTC markets, incorporating a practical default trigger mechanism. The default probability and the pricing formulae of the OTC options are obtained by using partial differential equation (PDE) techniques, especially Green’s function.     

An integrated multi-model credit rating system for private firms

This paper presents a integrated credit risk modelling approach for private firms which fulfil 2001 Basel Accord requirements in the case of the adoption of the foundation approach. Our model comprises: (a) a bottom-up technique to initially assess the through-the-cycle one-year Probability of Default (PD) and (b) a top-down approach to refine and calibrate this historical PD in a forward-looking credit risk assessment based on next year’s economic outlook. We present findings from applying this model to a large sample of client firms of the Bank of Rome.     

Credit risk,managerial behaviour and macroeconomic equilibrium within dual banking systems: Interest-free vs. interest-based banking industries

In this paper, an attempt has been made to explore the determinants of credit risk in the banking system with a particular interest toward the Islamic banking industry. We analyze the link between credit risk and a set of bank-specific and macroeconomic along with institutional variables using two complementary approaches. First, we investigate the factors of credit risk using one-step generalized method of moments (GMM) system estimator. Then, we explore the feedback between credit risk and its determinants in a panel vector autoregressive (PVAR) model. We have used a sample of Middle Eastern, North African (MENA) and Asian countries to apply our model. The major purpose of this paper is to find factors that could explain credit risk within the interest-free banking system relative to the interest-based one.     

Tempered stable structural model in pricing credit spread and credit default swap

In this paper, we explore the features of a structural credit risk model wherein the firm value is driven by normal tempered stable (NTS) process belonging to the larger class of Lévy processes. For the purpose of comparability, the calibration to the term structure of a corporate bond credit spread is conducted under both NTS structural model and Merton structural model. We find that NTS structural model provides better fit for all credit ratings than Merton structural model. However, it is noticed that probabilities of default derived from the calibration of the term structure of a bond credit spread might be overestimated since the bond credit spread could contain non-default components such as illiquidity risk or asymmetric tax treatment. Hence, considering CDS spread as a reflection of the pure credit risk for the reference entity, we calibrate it in order to obtain more reasonable probability of default and obtain valid results in calibration of the market CDS spread with NTS structural model.     

A new integral equation formulation for American put options

In this paper, a completely new integral equation for the price of an American put option as well as its optimal exercise price is successfully derived. Compared to existing integral equations for pricing American options, the new integral formulation has two distinguishable advantages: (i) it is in a form of one-dimensional integral, and (ii) it is in a form that is free from any discontinuity and singularities associated with the optimal exercise boundary at the expiry time. These rather unique features have led to a significant enhancement of the computational accuracy and efficiency as shown in the examples.     

The Allocation of Aggregate Risk,Secondary Market Trades,and Financial Boom–Bust Cycles

The financial crisis of 2007–08 started with the collapse of the market for collateralized debt obligations backed by subprime mortgages. In this paper we present a mechanism aimed at explaining how a freeze in a secondary debt market can be amplified and propagated to the real economy, and thereby cause a recession. Moreover, we show why such a process is likely to be especially strong after a prolonged expansion based on the growth of consumer credit and endogenously low risk premia. Hence, our model offers a new perspective on the links between the real and financial sectors, and we show how it can help make sense of several macro‐economic features of the 2001–09 period. The key elements of the model are heterogeneity across agents in terms of risk tolerance, a financial sector that allocates systematic risk efficiently across agents, and real decisions that depend on the price of risk.     

Managerial market timing under credit risk: How do timed buybacks and stock issuances influence the value of long-term shareholders?

Using discounted cash flow valuation together with a Merton-style credit risk model this paper quantifies the effects of credit risk on timed equity buybacks and issuances. Assumed managers act in best interest of their long-term shareholders and do have superior information, the potential value gain for long-term shareholders out of market timing with and without credit risk is evaluated. As demonstrated in a real-world example, credit risk is important. Ignoring credit risk results in value gains of buybacks motivated by smaller (larger) mispricing levels being underestimated (overestimated), while value gains of issuances driven by lower (larger) mispricings are overestimated (underestimated). These effects are stronger for firms with higher debt levels.     

Pricing the Risks of Default: A Note on Madan and Unal

In their well-known article, Madan and Unal (1998) presented one of the first intensity-based credit risk models. In this approach the default intensity is directly linked to the market value of the firm's equity. In order to derive the probability of default Madan and Unal have to solve a partial differential equation (PDE). Here, we show that one of the transformations in the derivation of the solution of this PDE is not correct and analyze the difference between the correct solution of the PDE and the solution based on the incorrect transformation. As a consequence of the transformation error the credit risk of a debtor is systematically underestimated.     

国外信用风险度量方法及其适用性研究

信用风险是银行面临诸多风险中最重要的风险,如何量化和控制信用风险一直是金融研究的热点领域之一。本文在对国外现代主流信用风险度量模型进行比较研究的基础上,分析了它们各自的特征和适用性,结合中资银行的特点,提出了适合我国国情的信用风险度量模型选取原则,基于我国现状建议在国内推广应用Logistic模型,以期对我国信用风险管理实务有一定的参考价值。     

Integrating Credit Models Using Accounting Information With Loan Officers' Decision Processes

This paper focuses on loan officers' cognitive processes of problem detection and problem-hypothesis formulation, which are incorporated into a credit model when they are confronted with loan decisions. Prior credit models in banking have not directly addressed loan officers' internal processes in a loan situation. The integration of both loan officers' cognitive processes and information used in a credit model can better help explain their decision-making biases. The results presented in this paper showed that information derived from a credit model influences loan officers' problem detection and problem-hypothesis formulation, and these processes are important factors in their loan approval. To identify loan officers' decision-making processes, the approach used in this paper integrates principles from financial management, economics, and cognitive psychology with methodological developments from psychometrics and econometrics.     

Credit risk transfer and financial sector stability

In this paper, we study credit risk transfer (CRT) in an economy with endogenous financing (by both banks and non-bank institutions). Our analysis suggests that the incentive of banks to transfer credit risk is aligned with the regulatory objective of improving stability, and so the recent development of credit derivative instruments is to be welcomed. Moreover, we find the transfer of credit risk from banks to non-banks to be more beneficial than CRT within the banking sector. Intuitively, this is because it allows for the shedding of aggregate risk which must otherwise remain within the relatively more fragile banking sector. Therefore, regulators should act to maximize the benefits from CRT by encouraging the development of instruments favorable to the cross-sectoral transfer of aggregate credit risk (including basket credit derivatives such as collateralized debt obligations). Finally, we derive the optimal regulatory stance for banks relative to non-bank financial institutions. We show that a level playing field approach is sub-optimal. Regulatory stances should be set to actively encourage cross-sector CRT, first because of the higher fragility of the banking sector and second to induce banks to incur the costs of CRT which otherwise lead them to undertake an insufficient amount of CRT.     

Pricing Derivatives using the Asymptotic Expansion Approach: Credit Migration Models with Stochastic Credit Spreads

The purpose of this paper is to evaluate the asymptotic approximation formulas for the price of contingent claims with credit risk, such as credit default swaps and options on defaultable bonds, in a Markovian credit migration model. Often the generator matrix of a credit migration process is assumed to be deterministic; however, a stochastically varying generator matrix is used in this paper. To apply such a model to the valuation of options on defaultable bonds, the small disturbance asymptotic expansion approach of Kunitomo and Takahashi is used in this study.