Assessing credit quality from the equity market: can a structural approach forecast credit ratings?

We investigate the empirical performance of default probability prediction based on Merton's (1974) structural credit risk model. More specifically, we study if distance‐to‐default is a sufficient statistic for the equity market information concerning the credit quality of the debt‐issuing firm. We show that a simple reduced form model outperforms the Merton (1974) model for both in‐sample fitting and out‐of‐sample predictability for credit ratings, and that both can be greatly improved by including the firm's equity value as an additional variable. Moreover, the empirical performance of this hybrid model is very similar to that of the simple reduced form model. As a result, we conclude that distant‐to‐default alone does not adequately capture the firm's credit quality information from the equity market. Copyright © 2007 ASAC. Published by John Wiley & Sons, Ltd.     

INCORPORATING RISK AND AMBIGUITY AVERSION INTO A HYBRID MODEL OF DEFAULT

It is well known that purely structural models of default cannot explain short‐term credit spreads, while purely intensity‐based models lead to completely unpredictable default events. Here we introduce a hybrid model of default, in which a firm enters a “distressed” state once its nontradable credit worthiness index hits a critical level. The distressed firm then defaults upon the next arrival of a Poisson process. To value defaultable bonds and credit default swaps (CDSs), we introduce the concept of robust indifference pricing. This paradigm incorporates both risk aversion and model uncertainty. In robust indifference pricing, the optimization problem is modified to include optimizing over a set of candidate measures, in addition to optimizing over trading strategies, subject to a measure dependent penalty. Using our model and valuation framework, we derive analytical solutions for bond yields and CDS spreads, and find that while ambiguity aversion plays a similar role to risk aversion, it also has distinct effects. In particular, ambiguity aversion allows for significant short‐term spreads.     

Implied deterministic volatility functions: An empirical test for Euribor options

This study proposes the implied deterministic volatility function (IDVF) for the volatility as the function of moneyness and time in the Heath, Jarrow, and Morton (1992) model to price and hedge Euribor options across moneyness and maturities from 1 January 2003 to 31 December 2005. The IDVF models are extended to two‐ and three‐factor models, indicating that they are potential candidates for interest rate risk management. Based on the criteria of in‐sample fitting, prediction, and hedging, it is found that two‐factor IDVF models provide the best in‐sample and prediction performance, whereas three‐factor IDVF models yield the best results for hedging. Correctly specified multifactor models with the volatility as the function of moneyness and time can replace inappropriate onefactor models. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:319–347, 2009     

DYNAMIC DEFAULTABLE TERM STRUCTURE MODELING BEYOND THE INTENSITY PARADIGM

The two main approaches in credit risk are the structural approach pioneered by Merton and the reduced‐form framework proposed by Jarrow and Turnbull and by Artzner and Delbaen. The goal of this paper is to provide a unified view on both approaches. This is achieved by studying reduced‐form approaches under weak assumptions. In particular, we do not assume the global existence of a default intensity and allow default at fixed or predictable times, such as coupon payment dates, with positive probability. In this generalized framework, we study dynamic term structures prone to default risk following the forward‐rate approach proposed by Heath, Jarrow, and Morton. It turns out that previously considered models lead to arbitrage possibilities when default can happen at a predictable time. A suitable generalization of the forward‐rate approach contains an additional stochastic integral with atoms at predictable times and necessary and sufficient conditions for an appropriate no‐arbitrage condition are given. For efficient implementations, we develop a new class of affine models that do not satisfy the standard assumption of stochastic continuity. The chosen approach is intimately related to the theory of enlargement of filtrations, for which we provide an example by means of filtering theory where the Azéma supermartingale contains upward and downward jumps, both at predictable and totally inaccessible stopping times.     

A two‐mean reverting‐factor model of the term structure of interest rates

This article presents a two‐factor model of the term structure of interest rates. It is assumed that default‐free discount bond prices are determined by the time to maturity and two factors, the long‐term interest rate, and the spread (i.e., the difference) between the short‐term (instantaneous) risk‐free rate of interest and the long‐term rate. Assuming that both factors follow a joint Ornstein‐Uhlenbeck process, a general bond pricing equation is derived. Closed‐form expressions for prices of bonds and interest rate derivatives are obtained. The analytical formula for derivatives is applied to price European options on discount bonds and more complex types of options. Finally, empirical evidence of the model's performance in comparison with an alternative two‐factor (Vasicek‐CIR) model is presented. The findings show that both models exhibit a similar behavior for the shortest maturities. However, importantly, the results demonstrate that modeling the volatility in the long‐term rate process can help to fit the observed data, and can improve the prediction of the future movements in medium‐ and long‐term interest rates. So it is not so clear which is the best model to be used. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23: 1075–1105, 2003     

Multifactor implied volatility functions for HJM models

This study evaluates two one‐factor, two two‐factor, and two three‐factor implied volatility functions in the HJM class, with the use of eurodollar futures options across both strike prices and maturities. The primary contributions of this article are (a) to propose and test three implied volatility multifactor functions not considered by K. I. Amin and A. J. Morton (1994), (b) to evaluate models using the AIC criteria as well as other standard criteria neglected by S. Y. M. Zeto (2002), and (c) to .nd that multifactor models incorporating the exponential decaying implied volatility functions generally outperform other models in .tting and prediction, in sharp contrast to K. I. Amin and A. J. Morton, who find the constantvolatility model superior. Correctly specified and calibrated simple constant and square‐root factor models may be superior to inappropriate multifactor models in option trading and hedging strategies. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:809–833, 2006     

TIME‐CHANGED MARKOV PROCESSES IN UNIFIED CREDIT‐EQUITY MODELING

This paper develops a novel class of hybrid credit‐equity models with state‐dependent jumps, local‐stochastic volatility, and default intensity based on time changes of Markov processes with killing. We model the defaultable stock price process as a time‐changed Markov diffusion process with state‐dependent local volatility and killing rate (default intensity). When the time change is a Lévy subordinator, the stock price process exhibits jumps with state‐dependent Lévy measure. When the time change is a time integral of an activity rate process, the stock price process has local‐stochastic volatility and default intensity. When the time change process is a Lévy subordinator in turn time changed with a time integral of an activity rate process, the stock price process has state‐dependent jumps, local‐stochastic volatility, and default intensity. We develop two analytical approaches to the pricing of credit and equity derivatives in this class of models. The two approaches are based on the Laplace transform inversion and the spectral expansion approach, respectively. If the resolvent (the Laplace transform of the transition semigroup) of the Markov process and the Laplace transform of the time change are both available in closed form, the expectation operator of the time‐changed process is expressed in closed form as a single integral in the complex plane. If the payoff is square integrable, the complex integral is further reduced to a spectral expansion. To illustrate our general framework, we time change the jump‐to‐default extended constant elasticity of variance model of Carr and Linetsky (2006) and obtain a rich class of analytically tractable models with jumps, local‐stochastic volatility, and default intensity. These models can be used to jointly price equity and credit derivatives.     

Asymmetric information and credit quality: Evidence from synthetic fixed‐rate financing

In this article the usage of synthetic fixed‐rate financing (SFRF) with interest rate swaps (i.e., borrowing short‐term and using swaps to hedge interest rate risk, instead of selecting conventional fixed‐rate financing) by Fortune 500 and S&P 500 nonfinancial firms is examined over the period 1991 through 1995. Credit ratings, debt issuance, and debt maturities of these firms are monitored through 1999. Strong evidence is found supporting the asymmetric information theory of swap usage as described by S. Titman (1992), even after controlling for industry, credit quality, size effects, and the simultaneity of the capital structure and the interest rate swap usage decision. Consistent with theoretical predictions, SFRF firms are more likely to undergo credit quality upgrades. When limiting the sample to firms where asymmetric information costs are potentially the greatest, the results are even stronger. These findings are important because they document that swaps serve a highly valuable service for firms subject to information asymmetries. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:595–626, 2006     

Network valuation in financial systems

We introduce a general model for the balance‐sheet consistent valuation of interbank claims within an interconnected financial system. Our model represents an extension of clearing models of interdependent liabilities to account for the presence of uncertainty on banks' external assets. At the same time, it also provides a natural extension of classic structural credit risk models to the case of an interconnected system. We characterize the existence and uniqueness of a valuation that maximizes individual and total equity values for all banks. We apply our model to the assessment of systemic risk and in particular for the case of stress testing. Further, we provide a fixed‐point algorithm to carry out the network valuation and the conditions for its convergence.     

BOUNDING WRONG‐WAY RISK IN CVA CALCULATION

A credit valuation adjustment (CVA) is an adjustment applied to the value of a derivative contract or a portfolio of derivatives to account for counterparty credit risk. Measuring CVA requires combining models of market and credit risk to estimate a counterparty's risk of default together with the market value of exposure to the counterparty at default. Wrong‐way risk refers to the possibility that a counterparty's likelihood of default increases with the market value of the exposure. We develop a method for bounding wrong‐way risk, holding fixed marginal models for market and credit risk and varying the dependence between them. Given simulated paths of the two models, a linear program computes the worst‐case CVA. We analyze properties of the solution and prove convergence of the estimated bound as the number of paths increases. The worst case can be overly pessimistic, so we extend the procedure by constraining the deviation of the joint model from a baseline reference model. Measuring the deviation through relative entropy leads to a tractable convex optimization problem that can be solved through the iterative proportional fitting procedure. Here, too, we prove convergence of the resulting estimate of the penalized worst‐case CVA and the joint distribution that attains it. We consider extensions with additional constraints and illustrate the method with examples.     

信用风险内部模型评价

随着金融风险数量化研究的深入与发展,研究者给出了形式各异的信用风险度量模型,这些模型依赖不同的假设和信用数据基础。如何在诸多模型中选择适用于自身风险度量的工作就显得十分重要。本文首先介绍Z-计分和EDF模型,然后利用AR方法对这些信用风险度量模型的预测精度进行比较分析,发现对于所选定样本AR值能较好的反映两个模型的预测精度。     

Multiple Ratings Model of Defaultable Term Structure

A new approach to modeling credit risk, to valuation of defaultable debt and to pricing of credit derivatives is developed. Our approach, based on the Heath, Jarrow, and Morton (1992) methodology, uses the available information about the credit spreads combined with the available information about the recovery rates to model the intensities of credit migrations between various credit ratings classes. This results in a conditionally Markovian model of credit risk. We then combine our model of credit risk with a model of interest rate risk in order to derive an arbitrage‐free model of defaultable bonds. As expected, the market price processes of interest rate risk and credit risk provide a natural connection between the actual and the martingale probabilities.     

Objective measures as a predictor of late payments by high‐risk borrowers

Manufactured homes (also known outside the US as prefabricated homes) are a viable housing option for low‐income buyers, but traditional mortgages are not available for purchase of manufactured homes because of a perception of higher risk of default among purchasers of manufactured homes. Research suggests that creditscoring models which incorporate objective data such as income, debt‐to‐income ratio and credit history result in an accurate and objective predictive tool to estimate likelihood of late payments and default among traditional home buyers. This study showed that these same models can be applied similarly to purchasers of manufactured homes. A Tobit model was developed to evaluate which factors most accurately predict default and late payment behaviour among borrowers who purchased a manufactured home. The model showed that when decomposed into the probability of making a late payment and number of late payments, credit score and income are both significant predictors in both sets of borrowers of both the probability of making a late payment and the number of late payments. The higher the credit score, the less likely the borrower is to make a late payment.     

Using Payment Behaviour Data for Credit Risk Modelling

In this paper we evaluate payment scores in two contexts; that of predicting future payment behaviour and that of corporate failure prediction. The assessment of the ability and willingness of a firm to pay its creditors, and the likely timeliness of payments, are a major focus of both credit risk analysis (from the trade credit perspective) and government policy, although the latter issues have not been much studied in the academic literature. While failure prediction models are traditionally used as indicators of payment behaviour in the UK, payment behaviour prediction models are estimated and made available in the USA by the leading credit reporting agencies and the predictive abilities of such scores in the UK context are, therefore, worthy of consideration.We also consider the contribution that payment behaviour scores can make to predicting corporate failure. An important question is whether the availability of payment behaviour scores increases the overall information content of the credit report or merely re-packages information represented elsewhere. We find that payment behaviour data can be used to predict successfully future payment behaviour in a trade credit context, and can add incrementally to the predictivity of corporate failure models.     

The Question of Sustainability for Microfinance Institutions*

Microentrepreneurs have considerable difficulty accessing capital from mainstream financial institutions. One key reason is that the costs of information about the characteristics and risk levels of borrowers are high. Relationship‐based financing has been promoted as a potential solution to information asymmetry problems in the distribution of credit to small businesses. In this paper, we seek to better understand the implications for providers of “microfinance” in pursuing such a strategy. We discuss relationship‐based financing as practiced by microfinance institutions (MFIs) in the United States, analyze their lending process, and present a model for determining the break‐even price of a microcredit product. Comparing the model’s results with actual prices offered by existing institutions reveals that credit is generally being offered at a range of subsidized rates to microentrepreneurs. This means that MFIs have to raise additional resources from grants or other funds each year to sustain their operations as few are able to survive on the income generated from their lending and related operations. Such subsidization of credit has implications for the long‐term sustainability of institutions serving this market and can help explain why mainstream financial institutions have not directly funded microenterprises. We conclude with a discussion of the role of nonprofit organizations in small business credit markets, the impact of pricing on their potential sustainability and self‐sufficiency, and the implications for strategies to better structure the credit market for microbusinesses.     

TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION

Expected utility models in portfolio optimization are based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance, and support information. No additional restrictions on the type of distribution such as normality is made. The investor’s utility is modeled as a piecewise‐linear concave function. We derive exact and approximate optimal trading strategies for a robust (maximin) expected utility model, where the investor maximizes his worst‐case expected utility over a set of ambiguous distributions. The optimal portfolios are identified using a tractable conic programming approach. Extensions of the model to capture asymmetry using partitioned statistics information and box‐type uncertainty in the mean and covariance matrix are provided. Using the optimized certainty equivalent framework, we provide connections of our results with robust or ambiguous convex risk measures, in which the investor minimizes his worst‐case risk under distributional ambiguity. New closed‐form results for the worst‐case optimized certainty equivalent risk measures and optimal portfolios are provided for two‐ and three‐piece utility functions. For more complicated utility functions, computational experiments indicate that such robust approaches can provide good trading strategies in financial markets.     

Competing Risk Model for Technology Credit Fund for Small and Medium‐Sized Enterprises

Despite the need to foster a technology‐intensive industry, most Korean SMEs (small and medium‐sized enterprises) are faced with the difficulty of raising funds. To resolve this problem, the government set up the technology credit fund to give loans to enterprises that achieve a certain technology evaluation score. However, many of the recipient SMEs fail to pay back the loans for various reasons. In this paper, we distinguish two causes of default due to owner and company, respectively, using the competing risk model. The proposed prediction models for competing defaults are expected to contribute to the healthy management of technology finance.     

Small Enterprise Default Prediction Modeling through Artificial Neural Networks: An Empirical Analysis of Italian Small Enterprises

Having accurate company default prediction models is vital for both banks and enterprises, especially small enterprises (SEs). These firms represent a vital part in the economy of every country but are also typically more informationally opaque than large corporations. Therefore, these models should be precise but also easily adaptable to suit SE characteristics. Our study applies artificial neural networks (ANNs) to a sample of over 7,000 Italian SEs. Results show that (1) when compared with traditional methods, ANNs can make a better contribution to SE credit‐risk evaluation; and (2) when the model is separately calculated according to size, geographical area, and business sector, ANNs prediction accuracy is markedly higher for the smallest sized firms and for firms operating in Central Italy.     

Trade Credit,Bank Credit,and Flight to Quality: Evidence from French SMEs

This paper investigates the impact of the global financial crisis on the allocation of credit to small and medium‐sized enterprises (SMEs). Using samples of French SMEs from four industries, we found support for the prediction of the flight‐to‐quality hypothesis that in bad times, credit flows away from smaller constrained firms to larger, higher grade firms. We also examined the relation between bank credit and trade credit in terms of two hypotheses: the substitution hypothesis and the complementary hypothesis. The results of fixed effects panel regressions showed that trade credit for small firms during periods of tight money acts generally as complement rather than substitute to bank credit, thus providing empirical support for the redistribution view of trade credit.     

Are credit spreads too low or too high? A hybrid barrier option approach for financial distress

Based on the works of Brockman, P. and Turtle, H. J. (2003) and Giesecke, K. (2004), we propose in this study a hybrid barrier option model to explain observed credit spreads. It is free of problems with the structural model, which underprescribed credit spreads for investment grade corporate bonds and overprescribed the high‐yield issues. Unlike the standard barrier option approach, our hybrid model does not imply, for high‐yield issues with firms under financial stress, a reduction of credit spreads while firm value actually falls. Our empirical analysis supports that when credit spreads are quoted abnormally higher or rising faster than expected, unexpected changes tend to persist. Otherwise a significant and prompt reversion to long‐term equilibrium takes place. This asymmetric pricing phenomenon is validated with a method introduced by Enders, W. and Granger, C. W. J. (1998) and Enders, W. and Siklos, P. L. (2001). The pricing asymmetry could not have been produced by a structural model employing only standard option. But it is consistent with a hybrid barrier option model. Our model characterizes the valuation of debt under financial stress and the asymmetric price pattern better than both the classical structural and the standard barrier option approaches. It can be extended to the study of individual CDS for its better liquidity than individual corporate bonds. This study provides helpful implications especially for the medium and high‐yield issues in pricing as well as portfolio diversification. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:1161–1189, 2009