An Estimation Model for the Term Structure of Yield Spread

An estimation model for term structure of yield spread has become an extremely important subject to evaluate securities with default risk. By Duffie and Singleton model, yield spread was explained by two factors, namely collection rate and default probability. An estimation of the collection rate is given from historical earnings data, but estimation of default probability is known to be a remaining problem.There are some approaches to express default probability. One of them is to describe it through hazard process, and the other is to represent it by risk neutral transition probability matrix of credit-rating class. Some models that use Gaussian type hazard process or Vasicek type hazard process have already constructed.An advantage of evaluation using a rating transition probability matrix is that it is easy to obtain an image of movement of the credit-rating class. We do not need to show the calculation basis of the threshold or an assumption for distribution of prospective yield spread. But the model that uses the risk neutral transition probability matrix has not established yet, because of the computational difficulty required to estimate large number of the parameters.At first, for the purposes of this article, we will estimate the term structure of credit spreads results from the possibility of future defaults. It is assumed that credit risk is specified as a discrete-state Markov chain. And we construct a model which can be used to estimate the baseline transition matrix of the credit-rating class, risk-adjusting factors, industrial drift factors, corporate drift factors and recovery ratio, from yield spreads for individual bond. This enables us to compute the implied term structure from market data. We are capable of computing the implied term structure from market date by this process. Next, we will provide a valuation model for the term structure of yield spread.     

Measuring Credit Risk of Individual Corporate Bonds in US Energy Sector

In this paper, using the measures of the credit risk price spread (CRiPS) and the standardized credit risk price spread (S-CRiPS) proposed in Kariya’s (A CB (corporate bond) pricing model for deriving default probabilities and recovery rates. Eaton, IMS Collection Series: Festschrift for Professor Morris L., 2013) corporate bond model, we make a comprehensive empirical credit risk analysis on individual corporate bonds (CBs) in the US energy sector, where cross-sectional CB and government bond price data is used with bond attributes. Applying the principal component analysis method to the S-CRiPSs, we also categorize individual CBs into three different groups and study on their characteristics of S-CRiPS fluctuations of each group in association with bond attributes. Secondly, using the market credit rating scheme proposed by Kariya et al. (2014), we make credit-homogeneous groups of CBs and show that our rating scheme is empirically very timely and useful. Thirdly, we derive term structures of default probabilities for each homogeneous group, which reflect the investors’ views and perspectives on the future default probabilities or likelihoods implicitly implied by the CB prices for each credit-homogeneous group. Throughout this paper it is observed that our credit risk models and the associated measures for individual CBs work effectively and can timely provide the market credit information evaluated by investors.     

How much of the corporate bond spread is due to personal taxes?

Existing term structure models of defaultable bonds have often underestimated corporate bond spreads. A potential problem is that investors’ taxes are ignored in these models. We propose a pricing model that accounts for stochastic default probability and differential tax treatments for discount and premium bonds. By estimating parameters directly from bond data, we obtain significantly positive estimates for the income tax rate of a marginal corporate bond investor after 1986. This contrasts sharply with the previous finding that the implied tax rates for Treasury bonds are close to zero. Results show that taxes explain a substantial portion of corporate bond spreads.     

中小企业集合债券总体信用风险度量研究

中小企业集合债券总体信用风险既包括系统风险产生的周期性违约风险,又包括相互关联关系导致的传染性违约风险。首先通过对因素模型的改进构建模型Ⅰ,研究集合债券的周期性违约风险;在此基础上引入违约传染建立模型Ⅱ,分析违约传染对违约概率及违约相关性的影响,研究集合债券的总体信用风险。最后基于模型Ⅱ进行算例研究,得出结论：企业间的相互关联关系降低了其1次违约概率,增加了其多次违约概率即违约相关性。     

Taxes,Default Risk,and Yield Spreads

This paper develops a model of bond prices and yield spreads that incorporates the effect of both taxes and differences in default probabilities. The tax loss consequences of default are recognized. Traditionally, tax-free (municipal) bond yields have been viewed as linearly related to taxable yields with a slope coefficient equal to one minus the tax rate and the intercept representing differences in default risk. While our model supports the linearity assumption, it implies that the slope and intercept are both functions of both the break-even tax rate and the default probability(ies). Clientele effects among both municipal and taxable bonds are demonstrated. Finally, the implied marginal tax rates and the implied default probabilities are estimated for different categories of municipal bonds.     

On the Term Structure of Default Premia in the Swap and LIBOR Markets

Existing theories of the term structure of swap rates provide an analysis of the Treasury–swap spread based on either a liquidity convenience yield in the Treasury market, or default risk in the swap market. Although these models do not focus on the relation between corporate yields and swap rates (the LIBOR–swap spread), they imply that the term structure of corporate yields and swap rates should be identical. As documented previously (e.g., in Sun, Sundaresan, and Wang (1993)) this is counterfactual. Here, we propose a model of the default risk imbedded in the swap term structure that is able to explain the LIBOR–swap spread. Whereas corporate bonds carry default risk, we argue that swap contracts are free of default risk. Because swaps are indexed on "refreshed"-credit-quality LIBOR rates, the spread between corporate yields and swap rates should capture the market's expectations of the probability of deterioration in credit quality of a corporate bond issuer. We model this feature and use our model to estimate the likelihood of future deterioration in credit quality from the LIBOR–swap spread. The analysis is important because it shows that the term structure of swap rates does not reflect the borrowing cost of a standard LIBOR credit quality issuer. It also has implications for modeling the dynamics of the swap term structure.     

我国企业债券违约的特征趋势、融资特点及风险处置机制研究

本文从债券违约的数量规模、行业分布、地域分布、企业属性、债券品种及违约率等方面阐述了我国企业债券违约的特征趋势,分析了我国企业债券违约的主要原因及其所呈现出来的融资特点,探讨了我国企业债券违约后的五种处置方式,认为我国债券违约风险处置机制还不完善,缺少独立法律制度、处置的市场化程度较低、投资者保护机制不健全、对发行人缺乏硬性约束,影响了违约债券的整体兑付水平,投资人利益难以得到有效维护。建议采取多种措施降低债券违约发生率、优化发行人融资结构、建立债券违约的市场化处置机制,以降低债券违约风险,推动债券市场健康发展。     

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.     

THE ANALYTICS OF RELATIVE HOLDING-PERIOD RISKS FOR BONDS

The relation between default risk measures and holding-period risk measures for bonds is confusing for bond investors. Past studies show that lower-credit-quality bonds exhibit lower holding-period risk. In this research I develop models to decompose the risk of corporate bonds and specify the conditions necessary for lower credit quality to result in lower holding-period risk measures. Additionally, I offer insight into the seemingly haphazard pattern of holding-period risk as related to credit quality.     

The role of asset payouts in the estimation of default barriers

In the barrier option model of corporate security valuation, the firm’s creditors impose a default-triggering barrier on the firm value to protect their claim. Two disputed issues in the literature are whether the implied default barrier is positive, and whether it is above or below the book value of the firm’s liabilities. We extend the model of Brockman and Turtle (2003) by embedding asset payouts in the valuation of shareholders’ equity. Using a sample of US stocks from the NYSE, AMEX, and NASDAQ exchanges, our paper exploits market and firm information to compute the implied default barrier for thirty 2-digit SIC groups, including industrials and banks. Our results show that the implied default barrier is lower than it is in the received literature, and it can be less than total liabilities, even zero for some firms. The implied physical default probabilities are significantly lower in the presence of payouts, providing a closer fit to the historical corporate default rates, particularly for issuers of speculative-grade bonds.     

A new way of looking at the risk in defined benefit pension plans

The portability feature of a defined contribution (DC) pension greatly reduces the risk to the accumulation of pension wealth. Conversely, defined benefit (DB) pensions have a variety of default risks that decrease the expected value of DB pension wealth. This paper examines those risks. Accrual of DB pension wealth is characterized in terms of purchases of risky bonds. Changing jobs triggers default on these bonds. Simulations are presented to show the potential loss in pension wealth from default. In addition, a methodology used to price corporate bonds is applied to generate estimates of the implied risk premiums of DB pension bonds over comparable riskless bonds.     

What drives corporate default risk premia? Evidence from the CDS market

This article studies the economic factors behind corporate default risk premia in Europe during the period 2006–2010. We employ information embedded in Credit Default Swap (CDS) contracts to quantify expected excess returns from the underlying bonds in market-wide default circumstances. We disentangle the compensation to investors for unexpected changes in the creditworthiness of the bond issuer from their remuneration for the risk that the bond's price will drop in the event of default. Our results show that the risk premia associated with systematic factors influencing default arrivals represent approximately 40% of total CDS spread (on median). These premia also exhibit a strong source of commonality; a single principal component explains approximately 88% of their joint variability. This factor significantly covaries with aggregate illiquidity and sovereign risk variables. Empirical evidence suggests a public-to-private risk transfer between sovereign credit spread and corporate risk premia. Finally, the compensation in the event of default is approximately 14 basis points of the total CDS spread, and a significant amount of jump-at-default risk may not be diversifiable.     

Liquidity,default, taxes,and yields on municipal bonds

We examine the effects of liquidity, default and personal taxes on the relative yields of Treasuries and municipals using a generalized model with liquidity risk. The municipal yield model includes liquidity as a state factor. Using a unique transaction dataset, we estimate the liquidity risk of municipals and its effect on bond yields. Empirical evidence shows that municipal bond yields are strongly affected by all three factors. The effects of default and liquidity risk on municipal yields increase with maturity and credit risk. Liquidity premium accounts for about 9–13% of municipal yields for AAA bonds, 9–15% for AA/A bonds and 8–19% for BBB bonds. A substantial portion of the maturity spread between long- and short-maturity municipal bonds is attributed to the liquidity premium. Ignoring the liquidity risk effect thus results in a severe underestimation of municipal bond yields. Conditional on the effects of default and liquidity risk, we obtain implicit tax rates very close to the statutory tax rates of high-income individuals and institutional investors. Furthermore, these implicit income tax rates are quite stable across bonds of different maturities. Results show that including liquidity risk in the municipal bond pricing model helps explain the muni puzzle.     

Bond Yields,Taxes, and the Dimensions of Default Risk

This work develops and empirically estimates models of bond yields subject to default risk. Parameters for the probability of survival and the recovery rate subsequent to default are included in a model of corporate bond yields that allow a study of interactions among them. The municipal version of the model includes the tax rate as an additional factor. Empirical evidence is found that supports the notion that both dimensions of default, considered jointly, are related to bond quality. In addition, statistically significant differences in tax rates suggest that higher tax rates are associated with higher grade municipal bonds.     

Underwriter reputation and the quality of certification: Evidence from high-yield bonds

This paper provides primary evidence of whether certification via reputable underwriters is beneficial to investors in the corporate bond market. We focus on the high-yield bond market in which certification of issuer quality is most valuable to investors owing to low liquidity and issuing firms’ high opacity and default risk. We find bonds underwritten by the most reputable underwriters to be associated with significantly higher downgrade and default risk. Investors seem to be aware of this relation, as we further find the private information conveyed via the issuer-reputable underwriter match to have a significantly positive effect on at-issue yield spreads. Our results are consistent with the market-power hypothesis, and contradict the traditional certification hypothesis and underlying reputation mechanism.     

A comparative study of the probability of default for global financial firms

This article presents a modification of Merton’s (1976) ruin option pricing model to estimate the implied probability of default from stock and option market prices. To test the model, we analyze all global financial firms with traded options in the US and focus on the subprime mortgage crisis period. We compare the performance of the implied probability of default from our model to the expected default frequencies based on the Moody’s KMV model and agency credit ratings by constructing cumulative accuracy profiles (CAP) and the receiver operating characteristic (ROC). We find that the probability of default estimates from our model are equal or superior to other credit risk measures studied based on CAP and ROC. In particular, during the subprime crisis our model surpassed credit ratings and matched or exceeded KMV in anticipating the magnitude of the crisis. We have also found some initial evidence that adding off-balance-sheet derivatives exposure improves the performance of the KMV model.     

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.      

Relative default rates on corporate loans and bonds

We use two alternative matched-set methodologies to examine for differences in loan and bond default rates among US non-financial corporate issuers. Under both methodologies, the data indicate that loan default rates are roughly 20% lower than the bond default rates due to issuers that default on their bonds but avoid bankruptcy and avoid defaulting on their loans. For a small number of European issuers, the data suggest a similar reduction in loan default rates relative to bond default rates. However, the European results differ qualitatively from the US results, due likely to differences in US and European bankruptcy regimes, as well as the larger role of bank debt on most European issuers’ balance sheets. These results have important implications for investors, bank supervisors, and rating agencies that assess the relative expected credit losses on loans versus bonds.     

A CERTAINTY EQUIVALENT APPROACH TO MUNICIPAL BOND DEFAULT RISK ESTIMATION

This paper extends the risk-neutrality default model of municipal bonds to consider the effect of risk aversion on the estimation of default probability. A model is proposed to separate the default risk assessment from the investor's risk aversion. Empirical results show that the risk-neutrality model consistently overestimates the default probability but that the magnitude of this overestimate is generally small and statistically insignificant.     

Effective duration of callable corporate bonds: Theory and evidence

This paper computes the effective duration of callable corporate bonds, using a contingent-claims model that incorporates both default risk and call risk. The model generates empirical implications regarding the cross-sectional variation and the firm-specific determinants of duration, and demonstrates that the effect of the call feature is to shorten duration (except for low-grade bonds). The effective duration is also estimated empirically for a large sample of long-term corporate bonds, using monthly bond price and interest rate data. Cross-sectional regression analysis is used to test the empirical implications of the model regarding the determinants of effective duration, and the empirical results are quite supportive of the model’s predictions.