Exploring the components of credit risk in credit default swaps

In this paper, we test the influence of various fundamental variables on the pricing of credit default swaps. The theoretical determinants that are important for pricing credit default swaps include the risk-free rate, industry sector, credit rating, and liquidity factors. We suggest a linear regression model containing these different variables, especially focusing on liquidity factors. Unlike bond spreads which have been shown to be inversely related to liquidity (i.e., the greater the liquidity, the lower the spread), there is no a priori reason that the credit default swap spread should exhibit the same relationship. This is due to the economic characteristics of a credit default swap compared to a bond. Our empirical result shows that all the fundamental variables investigated have a significant effect on the credit default swap spread. Moreover, our findings suggest that credit default swaps that trade with greater liquidity have a wider credit default swap spread.     

Pricing default swaps: Empirical evidence

In this paper we compare market prices of credit default swaps with model prices. We show that a simple reduced form model outperforms directly comparing bonds' credit spreads to default swap premiums. We find that the model yields unbiased premium estimates for default swaps on investment grade issuers, but only if we use swap or repo rates as proxy for default-free interest rates. This indicates that the government curve is no longer seen as the reference default-free curve. We also show that the model is relatively insensitive to the value of the assumed recovery rate.     

Empirical credit cycles and capital buffer formation

We model 1927–1997 US business failure rates using an unobserved components time series model. Clear evidence is found of cyclical behavior in default rates. We also detect significant longer term movements in default rates and default correlations. In a multi-year backtest experiment we show that accommodation of default rate dynamics has important consequences for credit risk capitalization requirements. Static or myopic variants of credit portfolio models miss significant periods of credit risk accumulation. Empirically congruent dynamic models by contrast provide more timely warning signals of credit risk build-up. In this way they may mitigate some of the pro-cyclicality concerns.     

Corporate bond default risk: A 150-year perspective

We study corporate bond default rates using an extensive new data set spanning the 1866-2008 period. We find that the corporate bond market has repeatedly suffered clustered default events much worse than those experienced during the Great Depression. For example, during the railroad crisis of 1873-1875, total defaults amounted to 36% of the par value of the entire corporate bond market. Using a regime-switching model, we examine the extent to which default rates can be forecast by financial and macroeconomic variables. We find that stock returns, stock return volatility, and changes in GDP are strong predictors of default rates. Surprisingly, however, credit spreads are not. Over the long term, credit spreads are roughly twice as large as default losses, resulting in an average credit risk premium of about 80 basis points. We also find that credit spreads do not adjust in response to realized default rates.     

Modelling bonds and credit default swaps using a structural model with contagion

This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default swap spreads and corporate bond yields. The credit dependence structure is influenced by both a longer-term correlation structure as well as by the possibility of default contagion. In this way, the model is able to generate a diverse range of shapes for the term structure of credit spreads using realistic values for input parameters.     

Credit risk assessment of fixed income portfolios using explicit expressions

We propose a model to assess the credit risk features of fixed income portfolios assuming they can be characterized by two parameters: their default probability and their default correlation. We rely on explicit expressions to assess their credit risk and demonstrate the benefits of our approach in a complex leveraged structure example. We show that using expected loss as a proxy for credit risk is misleading as it does not capture the dispersion effects introduced by correlation. The implications of these findings are relevant for improving current risk management practices and for regulation purposes.     

A set-valued Markov chain approach to credit default

We propose a novel credit default model that takes into account the impact of macroeconomic factors and intergroup contagion on the defaults of obligors. We use a set-valued Markov chain to model the default process, which includes all defaulted obligors in the group. We obtain analytic characterizations for the default process and derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs). Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupled with default contagion could have the leading component of the total default risk.     

A dynamic programming approach for pricing CDS and CDS options

We propose a flexible framework for pricing single-name knock-out credit derivatives. Examples include Credit Default Swaps (CDSs) and European, American and Bermudan CDS options. The default of the underlying reference entity is modelled within a doubly stochastic framework where the default intensity follows a CIR++ process. We estimate the model parameters through a combination of a cross sectional calibration-based method and a historical estimation approach. We propose a numerical procedure based on dynamic programming and a piecewise linear approximation to price American-style knock-out credit options. Our numerical investigation shows consistency, convergence and efficiency. We find that American-style CDS options can complete the credit derivatives market by allowing the investor to focus on spread movements rather than on the default event.     

Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity

We analyze the counterparty risk for credit default swaps using the Markov chain model of portfolio credit risk of multiple obligors with interacting default intensity processes. The default correlation between the protection seller and underlying entity is modeled by an increment in default intensity upon the occurrence of an external shock event. The arrival of the shock event is a Cox process whose stochastic intensity is assumed to follow an affine diffusion process with jumps. We examine how the correlated default risks between the protection seller and the underlying entity may affect the credit default premium in a credit default swap.     

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.      

基于Logistic模型的单个信用资产违约概率预测

在信用风险管理领域,由于中国商业银行信贷数据只满足Logistic模型的要求,因而预测单个信用资产违约率只能以Logistic模型为主线建模。以中国某商业银行1999~2005年的信贷数据为样本,实证分析得出,企业本身、宏观经济、地区及行业四方面因素对企业违约概率存在显著相关性。通过以上述四因素为变量,所构建的预测电力、公路、城镇建设三个行业信用资产违约概率的Logistic模型分析与预测单个信用资产违约的结果来看,四要素模型对中国商业银行的信用风险管理具有参照价值。     

Modeling CDS spreads: A comparison of some hybrid approaches

According to the credit risk model proposed by Cathcart and El-Jahel (2006), default can occur either expectedly, when a certain signaling variable breaches a lower barrier, or unexpectedly, as the first jump of a Poisson process, whose intensity depends on the signaling variable itself and on the interest rate. In the present paper we test the performances of such a model and of other three models generalized by it in fitting the term structure of credit default swap (CDS) spreads. In order to do so, we derive a semi-analytical formula for pricing CDSs and we use it to fit the observed term structures of 65 different CDSs. The analysis reveals that all the model parameters yield a relevant contribution to credit spreads. Moreover, if the dependence of the default intensity on both the signaling variable and the interest rate is removed, the pricing of CDSs becomes very simple, from both the analytical and the computational standpoint, while the goodness-of-fit is reduced by only a few percentage points. Therefore, when using the credit risk model proposed by Cathcart and El-Jahel (2006), assuming a constant default intensity provides an interesting and efficient compromise between parsimony and goodness-of-fit. Furthermore, by fitting the term structure of CDS spreads on a period of about twelve years, we find that the parameters of the model with constant default are rather stable over time, and the goodness-of-fit is maintained high.     

Evaluating the sovereign and household credit risk in Singapore: A contingent claims approach

This study evaluates the credit risk of the household and government (sovereign) sectors in Singapore using the contingent claims approach (CCA). The CCA model estimates the default probability of both sectors based on the market value of the assets and liabilities of the sectors. Compared to the traditional credit rating system, this model is able to provide numerical estimates of the exposures and default probabilities. We find that from the year 2000 to 2013, variations in the credit risk measures correspond to the economic growth of Singapore. In addition, we suggest that the main factor affecting the credit risks in the government and household sectors in Singapore is the volatility of the assets held by both sectors, given that the asset-to-distress barrier ratios are relatively stable over the past 14 years for both sectors.     

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.     

变量序别化在信用评分模型中的应用研究

本文通过将连续数值变量进行序别化转换赋值,并基于这些变量建立Log- it信用评分模型,通过使用统计量AUC值与条件熵比率来检验序别化转换前后所建立回归模型的违约预测力。结果发现,连续数值变量经序别化转换后可提高模型的违约预测力及其韧性。     

The effect of credit guarantees on credit availability and delinquency rates

We use new data to examine whether credit guarantees affect economic incentives and whether they affect the credit available to small- and medium-size enterprises (SMEs). We find that firms that have both guaranteed and non-guaranteed loans are 1.67% more likely to miss payments on their guaranteed loans, but are not more likely to default on these loans. These findings suggest that guarantees affect firms’ incentives to repay loans but not their long-term performance. We also find that firms selected into the guarantee programs are 1.17% more likely to default on their loans compared with similar firms that borrow without guarantees. Since we find evidence that long-term performance is not affected by guarantees, the higher default rates among firms selected into the guarantee programs must be the consequence of adverse selection. We also find that credit guarantees increase the aggregated amount of credit; in particular, one additional dollar of guarantees increases the total credit for SMEs by US$ 0.65.     

Predicting unlisted SMEs' default: Incorporating market information on accounting-based models for improved accuracy

The risk associated with lending to small businesses has become more important since regulations started obliging banks to use separate procedures in assessing SMEs' credit worthiness. However, current accounting-based models for SMEs do not account for the impact of market information on default prediction. We fill this gap in the literature by introducing a hybrid default prediction model for unlisted SMEs that uses market information of listed SMEs (comparable approach) alongside existing accounting information of unlisted SMEs. Our results suggest that the accuracy of this default prediction modelling approach in the hold-out sample, during the period of the financial crisis 2007-09 and for the entire sample-period, improves considerably. We conclude that the proposed hybrid model is a good replacement for existing standard accounting-based methods on SMEs' default prediction.     

Interacting default intensity with a hidden Markov process

In this paper we consider a reduced-form intensity-based credit risk model with a hidden Markov state process. A filtering method is proposed for extracting the underlying state given the observation processes. The method can be applied to a wide range of problems. Based on this model, we derive the joint distribution of multiple default times without imposing stringent assumptions on the form of default intensities. Closed-form formulas for the distribution of default times are obtained which are then applied to solve a number of practical problems such as hedging and pricing credit derivatives. The method and numerical algorithms presented can be applicable to various forms of default intensities.     

Pricing defaultable bonds: a middle-way approach between structural and reduced-form models

In this paper we present a valuation model that combines features of both the structural and reduced-form approaches for modelling default risk. We maintain the cause and effect or ‘structural’ definition of default and assume that default is triggered when a state variable reaches a default boundary. However, in our model, the state variable is not interpreted as the assets of the firm, but as a latent variable signalling the credit quality of the firm. Default in our model can also occur according to a doubly stochastic hazard rate. The hazard rate is a linear function of the state variable and the interest rate. We use the Cox et al. (A theory of the term structure of interest rates. Econometrica, 1985, 53(2), 385–407) term structure model to preclude the possibility of negative probabilities of default. We also horse race the proposed valuation model against structural and reduced-form default risky bond pricing models and find that term structures of credit spreads generated using the middle-way approach are more in line with empirical observations.     

基于KMV模型的上市中小企业信贷风险研究

本文利用改进的KMV模型,对我国上市中小企业2008-2011年的信贷风险进行实证分析,并对改进后的模型进行准确性研究。研究结果表明:上市中小企业资产规模对违约距离的影响具有不确定性,但效果也不明显;股价的波动也会影响到违约距离的大小,且两者的关系是负相关的。改进后的KMV模型计算出的违约距离能很好地对上市中小企业的信贷风险进行度量和判别,实证分析表明:上市中小企业的违约距离近年来呈下降趋势,信贷风险有增大的迹象。