Credit rating dynamics and Markov mixture models

Despite mounting evidence to the contrary, credit migration matrices, used in many credit risk and pricing applications, are typically assumed to be generated by a simple Markov process. Based on empirical evidence, we propose a parsimonious model that is a mixture of (two) Markov chains, where the mixing is on the speed of movement among credit ratings. We estimate this model using credit rating histories and show that the mixture model statistically dominates the simple Markov model and that the differences between two models can be economically meaningful. The non-Markov property of our model implies that the future distribution of a firm’s ratings depends not only on its current rating but also on its past rating history. Indeed we find that two firms with identical current credit ratings can have substantially different transition probability vectors. We also find that conditioning on the state of the business cycle or industry group does not remove the heterogeneity with respect to the rate of movement. We go on to compare the performance of mixture and Markov chain using out-of-sample predictions.     

Detecting structural breaks and identifying risk factors in hedge fund returns: A Bayesian approach

Extending previous work on asset-based style factor models, this paper proposes a model that allows for the presence of structural breaks in hedge fund return series. We consider a Bayesian approach to detecting structural breaks occurring at unknown times and identifying relevant risk factors to explain the monthly return variation. Exact and efficient Bayesian inference for the unknown number and positions of the breaks is performed by using filtering recursions similar to those of the forward–backward algorithm. Existing methods of testing for structural breaks are also used for comparison. We investigate the presence of structural breaks in several hedge fund indices; our results are consistent with market events and episodes that caused substantial volatility in hedge fund returns during the last decade.     

Bayesian inference for issuer heterogeneity in credit ratings migration

Rating transition matrices for corporate bond issuers are often based on fitting a discrete time Markov chain model to homogeneous cohorts. Literature has documented that rating migration matrices can differ considerably depending on the characteristics of the issuers in the pool used for estimation. However, it is also well known in the literature that a continuous time Markov chain gives statistically superior estimates of the rating migration process. It remains to verify and quantify the issuer heterogeneity in rating migration behavior using a continuous time Markov chain. We fill this gap in the literature. We provide Bayesian estimates to mitigate the problem of data sparsity. Default data, especially when narrowing down to issuers with specific characteristics, can be highly sparse. Using classical estimation tools in such a situation can result in large estimation errors. Hence we adopt Bayesian estimation techniques. We apply them to the Moodys corporate bond default database. Our results indicate strong country and industry effects on the determination of rating migration behavior. Using the CreditRisk+ framework, and a sample credit portfolio, we show that ignoring issuer heterogeneity can give erroneous estimates of Value-at-Risk and a misleading picture of the risk capital. This insight is consistent with some recent findings in the literature. Therefore, given the upcoming Basel II implementation, understanding issuer heterogeneity has important policy implications.     

Testing for rational bubbles in the presence of structural breaks: Evidence from nonstationary panels

This paper presents new results on the rational bubbles hypothesis for a panel of 18 OECD countries using the model developed by Campbell (2000). We provide an analysis of international data that exploits increased power deriving from the panel unit root and cointegration methodology, together with the flexibility of allowing explicitly for multiple endogenous structural breaks in the individual series. Differently from the time series methodology, the panel data approach allows for a global analysis of the financial crashes that are related to rational bubbles. We find strong evidence in favor of bubbles phenomena.     

Credit risk drivers: Evaluating the contribution of firm level information and of macroeconomic dynamics

Understanding if credit risk is driven mostly by idiosyncratic firm characteristics or by systematic factors is an important issue for the assessment of financial stability. By exploring the links between credit risk and macroeconomic developments, we observe that in periods of economic growth there may be some tendency towards excessive risk-taking. Using an extensive dataset with detailed information for more than 30 000 firms, we show that default probabilities are influenced by several firm-specific characteristics. When time-effect controls or macroeconomic variables are also taken into account, the results improve substantially. Hence, though the firms’ financial situation has a central role in explaining default probabilities, macroeconomic conditions are also very important when assessing default probabilities over time.     

Modelling the economic value of credit rating systems

In this paper we develop a model of the economic value of credit rating systems. Increasing international competition and changes in the regulatory framework driven by the Basel Committee on Banking Supervision (Basel II) called forth incentives for banks to improve their credit rating systems. An improvement of the statistical power of a rating system decreases the potential effects of adverse selection, and, combined with meeting several qualitative standards, decreases the amount of regulatory capital requirements. As a consequence, many banks have to make investment decisions where they have to consider the costs and the potential benefits of improving their rating systems. In our model the quality of a rating system depends on several parameters such as the accuracy of forecasting individual default probabilities and the rating class structure. We measure effects of adverse selection in a competitive one-period framework by parameterizing customer elasticity. Capital requirements are obtained by applying the current framework released by the Basel Committee on Banking Supervision. Results of a numerical analysis indicate that improving a rating system with low accuracy to medium accuracy can increase the annual rate of return on a portfolio by 30–40 bp. This effect is even stronger for banks operating in markets with high customer elasticity and high loss rates. Compared to the estimated implementation costs banks could have a strong incentive to invest in their rating systems. The potential of reduced capital requirements on the portfolio return is rather weak compared to the effect of adverse selection.     

Pitfalls and remedies in testing the calibration quality of rating systems

Testing calibration quality by means of backtesting is an integral part in the validation of credit rating systems. Against this background this paper provides a comprehensive overview of existing testing procedures. We study the procedures’ deficiencies theoretically and illustrate their impact empirically. Based on the insights gained therefrom, we develop enhanced hybrid testing procedures which turn out to be superior to the commonly applied methods. We also propose computationally efficient algorithms for our calibration tests. Finally, we are able to demonstrate empirically that our method outperforms existing tests in a scenario analysis using rating data of Moody’s.     

Credit default swap spreads and variance risk premia

We find that the firm-level variance risk premium has a prominent explanatory power for credit spreads in the presence of market- and firm-level control variables established in the existing literature. Such predictability complements that of the leading state variable—the leverage ratio—and strengthens significantly with a lower firm credit rating, longer credit contract maturity, and model-free implied variance. We provide further evidence that (1) the variance risk premium has a cleaner systematic component than implied variance or expected variance, (2) the cross-section of firms’ variance risk premia capture systematic variance risk in a stronger way than firms’ equity returns in capturing market return risk, and (3) a structural model with stochastic volatility can reproduce the predictability pattern of variance risk premia for credit spreads.     

Greasing the wheels of bank lending: Evidence from private firms in China

Bribery, rather than firm performance, largely determines the extent to which private firms access bank credit in China. Bribery enables an economic outcome whereby firms with better economic performance are awarded larger loans. These firms also pay more in terms of bribes. Although satisfactory firm performance does determine whether firms can access loans, it does so only for loans originated by the big-four banks. For loans originated by smaller banks, performance is not essential for firms to secure loan access. Our evidence sheds light on the surprising finding of earlier studies that Chinese banks use commercial logic in their lending practices despite being endowed with a weak institutional framework.     

Estimation of continuous-time models with an application to equity volatility dynamics

The treatment of this article renders closed-form density approximation feasible for univariate continuous-time models. Implementation methodology depends directly on the parametric-form of the drift and the diffusion of the primitive process and not on its transformation to a unit-variance process. Offering methodological convenience, the approximation method relies on numerically evaluating one-dimensional integrals and circumvents existing dependence on intractable multidimensional integrals. Density-based inferences can now be drawn for a broader set of models of equity volatility. Our empirical results provide insights on crucial outstanding issues related to the rank-ordering of continuous-time stochastic volatility models, the absence or presence of nonlinearities in the drift function, and the desirability of pursuing more flexible diffusion function specifications.     

Variations in sovereign credit quality assessments across rating agencies

We investigate agency variation in credit quality assessment (Standard and Poor’s vs. Moody’s vs. Fitch) employing sovereign ratings data for 129 countries, spanning the period 1990–2006. While we find that the credit rating agencies often disagree about credit quality, it is usually confined to one or two notches on the finer scale. We find that several variables have varying importance in explaining ratings across agencies which leads us to conclude that material heterogeneity exists between them. Also, while watch and outlook procedures are generally strong predictors of rating changes relative to other public data, additional significant variables suggest that it might be possible to augment these agency data to provide better forecasts of future rating changes.     

Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity

We propose a model where wholesale electricity prices are explained by two state variables: demand and capacity. We derive analytical expressions to price forward contracts and to calculate the forward premium. We apply our model to the PJM, England and Wales, and Nord Pool markets. Our empirical findings indicate that volatility of demand is seasonal and that the market price of demand risk is also seasonal and positive, both of which exert an upward (seasonal) pressure on the price of forward contracts. We assume that both volatility of capacity and the market price of capacity risk are constant and find that, depending on the market and period under study, it could either exert an upward or downward pressure on forward prices. In all markets we find that the forward premium exhibits a seasonal pattern. During the months of high volatility of demand, forward contracts trade at a premium. During months of low volatility of demand, forwards can either trade at a relatively small premium or, even in some cases, at a discount, i.e. they exhibit a negative forward premium.     

Cyclicality in catastrophic and operational risk measurements

Using equity returns for financial institutions we estimate both catastrophic and operational risk measures over the period 1973–2003. We find evidence of cyclical components in both the catastrophic and operational risk measures obtained from the generalized Pareto distribution and the skewed generalized error distribution. Our new, comprehensive approach to measuring operational risk shows that approximately 18% of financial institutions’ returns represent compensation for operational risk. However, depository institutions are exposed to operational risk levels that average 39% of the overall equity risk premium. Moreover, operational risk events are more likely to be the cause of large unexpected catastrophic losses, although when they occur, the losses are smaller than those resulting from a combination of market risk, credit risk or other risk events.     

Detecting the presence of insider trading via structural break tests

The occurrence of abnormal returns before the unscheduled announcement of price sensitive information is a potential indicator of insider trading. We identify insider trading with a structural change in the intercept of an extended capital asset pricing model. To detect such a change we introduce a consistent timing structural break test (CTSB) based upon a U-statistic type process. Unlike the traditional CUSUM test, the CTSB test provides a consistent estimator of the timing of a break in the intercept that occurs across the whole evaluation period. We apply our test to a rich data set covering 370 price sensitive announcements relating to FTSE 350 companies. Our test is able to detect potential insider trading far more reliably than the standard CUSUM test. We also show that the majority of suspected insider trading takes place in the 25 days prior to the release of market sensitive information.     

Inference in asset pricing models with a low-variance factor

This paper concerns with the effects of including a low-variance factor in an asset pricing model. When a low-variance factor is present, the commonly applied Fama–MacBeth two-pass regression procedure is very likely to yield misleading results. Local asymptotic analysis and simulation evidence indicate that the risk premiums corresponding to all factors are very likely to be unreliably estimated. Moreover, t- and F-statistics are less likely to detect whether the risk premiums are significantly different from zero. We recommend Kleibergen’s (2009)FAR statistic when there is a low-variance factor included in an asset pricing model.     

Identifying volatility risk premia from fixed income Asian options

Fixed income options are frequently adopted by companies to hedge interest rate risk. Their payoff dependence on the cumulative short-term rate makes them particularly informative about interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate options, we study the interrelations between bond and volatility risk premia in a major emerging fixed income market. We propose a dynamic term structure model that generates an incomplete market compatible with a preliminary empirical analysis of the dataset. Approximation formulas for at-the-money Asian option prices avoid the use of computationally intensive Fourier transform methods, allowing for an efficient implementation of the model. The model generates a bond risk premium strongly correlated with a widely accepted emerging market benchmark index (EMBI-Global), and a negative volatility risk premium, consistent with the use of Asian options as insurance in this market.     

Are interest rate options important for the assessment of interest rate risk?

Fixed income options contain substantial information on the price of interest rate volatility risk. In this paper, we ask if those options will also provide information related to other moments of the objective distribution of interest rates. Based on dynamic term structure models within the class of affine models, we find that interest rate options are useful for the identification of interest rate quantiles. Two three-factor models are adopted and their adequacy to estimate Value at Risk of zero-coupon bonds is tested. We find significant difference on the quantitative assessment of risk when options are (or not) included in the estimation process of each of these dynamic models. Statistical backtests indicate that bond estimated risk is clearly more adequate when options are adopted, although not yet completely satisfactory.     

On the robustness of higher-moment factors in explaining average expected returns: Evidence from Australia

This study tests the importance of systematic skewness and systematic kurtosis of Australian stock returns in the spirit of the higher-moment asset pricing model. We apply the Dagenais and Dagenais (1997) higher-moment estimators to correct for the errors-in-variables (EIVs) problems commonly found in the Fama and MacBeth (1973) two-pass regression methodology. After correcting for the EIVs problems, the two higher-moment factors, especially systematic skewness, are important in pricing Australian stocks. Systematic kurtosis appears to replace beta which plays a diminished role in the heavy-tailed return distribution.     

The delivery option in credit default swaps

Under standard assumptions the reduced-form credit risk model is not capable of accurately pricing the two fundamental credit risk instruments – bonds and credit default swaps (CDS) – simultaneously. Using a data set of euro-denominated corporate bonds and CDS our paper quantifies this mispricing by calibrating such a model to bond data, and subsequently using it to price CDS, resulting in model CDS spreads up to 50% lower on average than observed in the market. An extended model is presented which includes the delivery option implicit in CDS contracts emerging since a basket of bonds is deliverable in default. By using a constant recovery rate standard models assume equal recoveries for all bonds and hence zero value for the delivery option. Contradicting this common assumption, case studies of Chapter 11 filings presented in the paper show that corporate bonds do not necessarily trade at equal levels following default. Our extension models the implied expected recovery rate of the cheapest-to-deliver bond and, applied to data, largely eliminates the mispricing. Calibrated recovery values lie between 8% and 47% for different obligors, exhibiting strong variation among rating classes and industries. A cross-sectional analysis reveals that the implied recovery parameter depends on proxies for the delivery option, primarily the number of available bonds and bond pricing errors. No evidence is found for a direct influence of the bid-ask spread, notional amount, coupon, or rating used as proxies for bond market liquidity.     

Option-implied volatility factors and the cross-section of market risk premia

The main goal of this paper is to study the cross-sectional pricing of market volatility. The paper proposes that the market return, diffusion volatility, and jump volatility are fundamental factors that change the investors’ investment opportunity set. Based on estimates of diffusion and jump volatility factors using an enriched dataset including S&P 500 index returns, index options, and VIX, the paper finds negative market prices for volatility factors in the cross-section of stock returns. The findings are consistent with risk-based interpretations of value and size premia and indicate that the value effect is mainly related to the persistent diffusion volatility factor, whereas the size effect is associated with both the diffusion volatility factor and the jump volatility factor. The paper also finds that the use of market index data alone may yield counter-intuitive results.