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.      

A first-passage-time model under regime-switching market environment

In this paper, we suggest a first-passage-time model which can explain default probability and default correlation dynamics under stochastic market environment. We add a Markov regime-switching market condition to the first-passage-time model of Zhou [Zhou, C., 2001. An analysis of default correlations and multiple defaults. Review of Financial Studies 14, 555–576]. Using this model, we try to explain various relationship between default probability, default correlation, and market condition. We also suggest a valuation method for credit default swap (CDS) with (or without) counterparty default risk (CDR) and basket default swap under this model.Our numerical results provide us with several meaningful implications. First, default swap spread is higher in economic recession than in economic expansion across default swap maturity. Second, as the difference of asset return volatility between under bear market and under bull market increases, CDS spread increases regardless of maturity. Third, the bigger the intensity shifting from bull market to bear market, the higher the spread for both CDS without CDR and basket default swap.     

Pricing Sovereign Credit Risk of Poland: Evidence from the CDS Market

We analyze the market assessment of sovereign credit risk using a reduced-form model to price the credit default swap (CDS) spreads, thus enabling us to derive values for the probability of default (PD) and loss given default (LGD) from the quotes of sovereign CDS contracts. We compare different specifications of the models allowing for both fixed and time-varying LGD, and we use these values to analyze the sovereign credit risk of Polish debt throughout the period of a global financial crisis. Our results suggest the presence of a low LGD and a relatively high PD during a recent financial crisis.     

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.     

Cross-hedging strategies between CDS spreads and option volatility during crises

This paper presents a joint analysis of the term structure of credit default swap (CDS) spreads and the implied volatility surface for five European countries from 2007 to 2012, a sample period covering both the Global Financial Crisis (GFC) and the European debt crisis. We analyze to which extent effective cross-hedges can be performed between the credit and equity derivatives markets during these two crises. We find that during a global crisis a breakdown of the relationship between credit risk and equity volatility may occur, jeopardizing any cross-hedging strategy, which happened during the GFC. This stands in sharp contrast to the more localized European debt crisis, during which this fundamental relationship was preserved despite turbulent market conditions for both the CDS and volatility markets.     

Modeling the evolution of implied CDO correlations

CDO tranche spreads (and prices of related portfolio-credit derivatives) depend on the market’s perception of the future loss distribution of the underlying credit portfolio. Applying Sklar’s seminal decomposition to the distribution of the vector of default times, the portfolio-loss distribution derived thereof is specified through individual default probabilities and the dependence among obligors’ default times. Moreover, the loss severity, specified via obligors’ recovery rates, is an additional determinant. Several (specifically univariate) credit derivatives are primarily driven by individual default probabilities, allowing investments in (or hedging against) default risk. However, there is no derivative that allows separately trading (or hedging) default correlations; all products exposed to correlation risk are contemporaneously also exposed to default risk. Moreover, the abstract notion of dependence among the names in a credit portfolio is not directly observable from traded assets. Inverting the classical Vasicek/Gauss copula model for the correlation parameter allows constructing time series of implied (compound and base) correlations. Based on such time series, it is possible to identify observable variables that describe implied correlations in terms of a regression model. This provides an economic model of the time evolution of the market’s view of the dependence structure. Different regression models are developed and investigated for the European CDO market. Applications and extensions to other markets are discussed.     

Credit derivatives: international developments and lessons for India

Credit derivatives have been popular instruments for hedging of credit risks by banks and financial institutions. The notional value outstanding of credit default swap contracts, a type of credit derivative most in use, increased from US$6.4 trillion in December 2004 to US$57.89 trillion in December, 2007. However, this instrument, which was once ‘apple of the eye’ of market players, lost its sheen in the wake of the sub-prime crisis when it was perceived to have played a major role in igniting the crisis and spreading it across the global financial system. This article presents how this came about and the after thought of the regulators of developed countries in regulating these instruments. It then looks at what lessons India can draw from the experience of the Western nations before considering introduction of credit derivatives in the Indian markets.     

Using extreme value theory to estimate the likelihood of banking sector failure

Abstract

The growing interest in management of credit risk and estimation of default probabilities has given rise to a range of more or less elaborate credit risk models. While these models work well for non-financial firms they are usually not very successful in capturing the financial strength of banks. As an answer to this, Hall and Miles suggest a simple approach of estimating bank failure probabilities based solely on their stock prices. This paper suggests an extension to the Hall and Miles model using extreme value theory and applies the extended model to the Swedish banking sector around the banking crisis of the early 1990s. The extended model captures very well the increased likelihood of a systemic banking sector failure around the peak of the crisis and it produces default probabilities that are more stable, more realistic and more consistent with Moody’s and Fitch rating implied default rates than probabilities from the original Hall and Miles model.     

Computing the survival probability in the Madan–Unal credit risk model: application to the CDS market

We obtain a quasi-analytical approximation of the survival probability in the credit risk model proposed in [Madan, D.B. and Unal, H., Pricing the risk of default. Rev. Deriv. Res., 1998, 2(2), 121–160]. Such a formula, which extensive numerical simulations reveal to be accurate and computationally fast, can also be employed for pricing credit default swaps (CDSs). Specifically, we derive a quasi-analytical approximate expression for CDS par spreads, and we use it to estimate the parameters of the model. The results obtained show a rather satisfactory agreement between theoretical and real market data.     

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.     

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.     

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.     

Credit Events and the Valuation of Credit Derivatives of Basket Type

Thispaper provides a simple model for valuing a credit derivativewhose payoff depends on the identity (or identities) of the first(or first two) to occur of a given list of credit events, suchas defaults. The joint survival probability of occurrence timesof credit events is formulated in terms of stochastic intensityprocesses under the assumption of conditional independence. Basedon the joint survival probability, we can easily obtain the pricingformulas of such credit derivatives under the risk-neutral valuationframework. When the default intensity processes follow the extendedVasicek model, closed-form solutions of the pricing formulasare given.     

Large EU banks’ capital and liquidity: Relationship and impact on credit default swap spreads

This paper explores the interrelations between bank capital and liquidity and their impact on the market probability of default. We employ an unbalanced panel of large European banks with listed credit default swap (CDS) contracts during the period 2005–2015, which allow us to consider the impact of the recent financial crisis. Our evidence suggests that bank capital and funding liquidity risk as defined in Basel III have an economically meaningful bidirectional relationship. However, the effect on CDS spread is ambiguous. While capital appears to have a relatively large impact on CDS spread changes, liquidity risk is priced only when it falls below the regulatory threshold.     

An Empirical Comparison of Credit Spreads between the Bond Market and the Credit Default Swap Market

This paper compares the pricing of credit risk in the bond market and the fast-growing credit default swap (CDS) market. The cointegration test confirms that the theoretical parity relationship between the two credit spreads holds as a long-run equilibrium condition. Nevertheless, substantial deviation from the parity can arise in the short run. The panel data study and the VECM analysis both suggest that the deviation is largely due to the higher responsiveness of CDS premia to changes in credit conditions. Moreover, it exhibits a certain degree of persistence in that only 10% of price discrepancies can be removed within a business day.     

债券违约对流动性影响的传染效应研究

2014年以来我国信用债市场违约事件频发,信用风险的积聚可能引发债券市场流动性恶化。本文以2014―2019年交易所和银行间市场信用债为研究对象,实证考察违约事件对债券流动性影响的传染效应。研究发现:违约事件在同一发行主体的债券之间具有流动性传染效应,当公司的某期债券出现违约时,公司其他未到期债券的流动性水平显著下降;违约事件对同行业其他公司债券的流动性具有传染效应,当行业中出现债券违约事件时,行业内其他公司的债券流动性显著降低;违约事件爆发越密集或者违约事件越严重,对债券流动性的负面影响越大,而且民营企业债受到的影响要大于国有企业债,低信用等级债受到的影响要大于高信用等级债;在市场密集爆发违约事件或出现较为严重的违约事件时期,宏观流动性增加能够改善债券流动性。     

An Empirical Investigation of CDS Spreads Using a Regime-Switching Default Risk Model

Default risk in equity returns can be measured by structural models of default. In this article we propose a credit warning signal (CWS) based on the Merton Default Risk (MDR) model and a Regime-Switching Default Risk (RSDR) model. The RSDR model is a generalization of the MDR model, comprises regime-switching asset distribution dynamics, and thus produces more realistic default probability estimates in cases of deteriorating credit quality. Alternatively, it reduces to the MDR model. Using a dataset of U.S. credit default swap (CDS) contracts around the 2007-8 crisis we construct rating-based indices to investigate the MDR and RSDR implied probabilities of default in relation to the market-observed CDS spreads. The proposed CWS measure indicates an increase in implied default probabilities several months ahead of notable increases in CDS spreads.     

Did the Market Signal Impending Problems at Northern Rock? An Analysis of Four Financial Instruments

The academic literature has regularly argued that market discipline can support regulatory authority mechanisms in ensuring banking sector stability. This includes, amongst other things, using forward‐looking market prices to identify those credit institutions that are most at risk of failure. The paper's key aim is to analyse whether market investors signalled potential problems at Northern Rock in advance of the bank announcing that it had negotiated emergency lending facilities at the Bank of England in September 2007. A further aim of the paper is to examine the signalling qualities of four financial market instruments (credit default swap spreads, subordinated debt spreads, implied volatility from options prices and equity measures of bank risk) so as to explore both the relative and individual qualities of each. The paper's findings, therefore, contribute to the market discipline literature on using market data to identify bank risk‐taking and enhancing supervisory monitoring. Our analysis suggests that private market participants did signal impending financial problems at Northern Rock. These findings lend some empirical support to proposals for the supervisory authorities to use market information more extensively to improve the identification of troubled banks. The paper identifies equities as providing the timeliest and clearest signals of bank condition, whilst structural factors appear to hamper the signalling qualities of subordinated debt spreads and credit default swap spreads. The paper also introduces idiosyncratic implied volatility as a potentially useful early warning metric for supervisory authorities to observe.     

Pricing the Credit Risk of Secured Debt and Financial Leasing

Abstract:  This paper presents closed form solutions to price secured bank loans and financial leases subject to default risk. Secured debt fair credit spreads always increase in the debtor's default probability, whereas financial leasing fair credit spreads may well decrease in the lessee's default probability and even be negative. The reason is that the lessor, unlike the secured lender, can gain from the lessee's default, especially when the leasing contract envisages initial prepayments or the lessee's terminal options to either purchase the leased asset or to extend the lease maturity. This result, which critically depends on contractual and bankruptcy code provisions, can explain some of the empirical evidence and the use of financial leases as an alternative to secured bank lending to finance small, risky and relatively opaque firms.     

基于会计信息的KMV模型实证研究

本文借助KMV模型框架,运用统计方法对大量的公司财务报表数据进行模型参数估计,计算得到了非上市公司的违约距离和经验EDF函数,实现了违约概率的模型估计。实证表明,我国公司在违约距离或违约数量上的真实概率分布均呈现显著的T分布和肥尾特性;违约距离具有较高的风险区分能力;由会计信息进行参数估计的模型导出的EDF具有较高的风险标识精度;进而表明基于会计报表数据的违约风险模型和基于资本市场数据的模型在实证上的有效性非常近似。