A Markov model for the term structure of credit risk spreads

This article provides a Markov model for the term structureof credit risk spreads. The model is based on Jarrow and Turnbull(1995), with the bankruptcy process following a discrete statespace Markov chain in credit ratings. The parameters of thisprocess are easily estimated using observable data. This modelis useful for pricing and hedging corporate debt with imbeddedoptions, for pricing and hedging OTC derivatives with counterpartyrisk, for pricing and hedging (foreign) government bonds subjectto default risk (e.g., municipal bonds), for pricing and hedgingcredit derivatives, and for risk management.     

An analysis of default correlations and multiple defaults

Evaluating default correlations or the probabilities of defaultby more than one firm is an important task in credit analysis,derivatives pricing, and risk management. However, default correlationscannot be measured directly, multiple-default modeling is technicallydifficult, and most existing credit models cannot be appliedto analyze multiple defaults. This article develops a first-passage-timemodel, providing an analytical formula for calculating defaultcorrelations that is easily implemented and conveniently usedfor a variety of financial applications. The model also providesa theoretical justification for several empirical regularitiesin the credit risk literature.     

The analytic pricing of asymmetric defaultable swaps

Swaps where both parties are exposed to credit risk still lack convincing pricing mechanisms. This article presents a reduced-form model where the event of default is related to structural characteristics of each party. The cash flows submitted to credit risk are identified before the swap is priced. Analytical pricing formulas for interest rate and currency swaps are computed using a Gaussian model for risky bonds. Currency swaps exhibit additional correlation risk. The benefits from netting depend on the balance between exposures and market conditions in valuation. We show that sources of credit risk asymmetries are also likely to impact on credit spreads.     

信用违约风险传染模型的比较研究

本文试图对几种有代表性的模型进行比较,来分析由于建模方式的不同,而导致的对信用期权定价和对冲的结果的不同.如果将违约风险传染考虑进去,类似德隆帝国崩溃的事件,或许就能避免.     

Credit risk modeling with affine processes

This article combines an orientation to credit risk modeling with an introduction to affine Markov processes, which are particularly useful for financial modeling. We emphasize corporate credit risk and the pricing of credit derivatives. Applications of affine processes that are mentioned include survival analysis, dynamic term-structure models, and option pricing with stochastic volatility and jumps. The default-risk applications include default correlation, particularly in first-to-default settings. The reader is assumed to have some background in financial modeling and stochastic calculus.     

The Credit Risk and Pricing of OTC Options

In the over-the-counter (OTC) markets, the options traded are always subject to credit risk. Therefore the counterparty’s credit risk is a striking factor when pricing options, whereas it is not considered in the classic Black-Scholes models. Based on the first passage time models, this paper develops the credit risk and valuation model for the European options in the OTC markets, incorporating a practical default trigger mechanism. The default probability and the pricing formulae of the OTC options are obtained by using partial differential equation (PDE) techniques, especially Green’s function.     

How well do classical credit risk pricing models fit swap transaction data?

Currency and interest rate swaps are subject to a complex, two-sided default risk. Several theoretical papers have recently addressed the problem of pricing this swap credit risk. We implement a recent credit risk pricing model in an attempt to evaluate one of the main lines of research in theoretical credit risk analysis. We compare the model's analytical results to actual transaction data thanks to a unique academic database on swap transaction data.     

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.     

Implied migration rates from credit barrier models

The risk-neutral credit migration process captures quantitative information which is relevant to the pricing theory and risk management of credit derivatives. In this article, we derive implied migration rates by means of a recently introduced credit barrier model which is calibrated on the basis of aggregate information such as credit migration rates and credit spread curves. The model is characterized by an underlying stochastic process that represents credit quality, and default events are associated to barrier crossings. The stochastic process has state dependent volatility and jumps which are estimated by using empirical migration and default rates. A risk-neutralizing drift and forward liquidity spreads are estimated to consistently match the average spread curves corresponding to all the various ratings. The implied migration rates obtained with our credit barrier model are then compared with those obtained via the Kijima–Komoribayashi model.     

Modeling the business risk of financially weakened firms: A new approach for corporate bond pricing

Most structural models of default risk assume that the firm's asset return is normally distributed, with a constant volatility. By contrast, this article details the properties that the process of assets should have in the case of financially weakened firms. It points out that jump-diffusion processes with time-varying volatility provide a refined and accurate perspective on the business risk dimension of default risk. Representative Arrow-Debreu state price densities (SPD) and term structures of credit spreads are then explored. The credit curves show that the business uncertainties play a major in the pricing of corporate liabilities.     

Pricing Derivatives on Financial Securities Subject to Credit Risk

This article provides a new methodology for pricing and hedging derivative securities involving credit risk. Two types of credit risks are considered. The first is where the asset underlying the derivative security may default. The second is where the writer of the derivative security may default. We apply the foreign currency analogy of Jarrow and Turnbull (1991) to decompose the dollar payoff from a risky security into a certain payoff and a “spot exchange rate.” Arbitrage-free valuation techniques are then employed. This methodology can be applied to corporate debt and over the counter derivatives, such as swaps and caps.     

A Note on Credit Risk of Vertical <Emphasis Type="Italic">Keiretsu</Emphasis> Firms: Preliminary Evidence from the Japanese Automobile Industry

This paper empirically examines the relationship between the credit risk of Toyota, Nissan and Honda keiretsu-affiliated firms and the credit risk of the respective parent company. As credit spread data for keiretsu-affiliated firms were not available we create a keiretsu default index, as a proxy, using expected default probabilities obtained from the KMV and Leland and Toft (J. Finance 51, 987–1019, 1996) option pricing models. We find parent credit spreads do not Granger cause our keiretsu default index and vice versa in a bivariate vector autoregressive (VAR) framework.JEL classification: G3, L62     

信用风险缓释工具定价研究

通过对信用风险缓释工具定价进行研究得出:(1)CRM定价的主要影响因素包括无风险基准利率,标的债券的风险敞口、违约概率、违约损失率和期限,以及CRM期限等。(2)同期国债利率和央行票据利率作为CRM的基准利率较为恰当,且模型定价对不同期限、不同信用等级的CRM定价区分度较为合理,模型定价与CRM发行交易定价较为接近,适合我国现阶段CRM产品定价。(3)可以从完善CRM定价基础数据库、探索CRM定价无风险基础利率、创新CRM标的债券评级制度、引导CRM市场主体多元化和优化CRM市场做市商制度等方面提出CRM定价优化对策。     

Credit derivatives with multiple debt issues

We evaluate the most actively traded types of credit derivatives within a unified pricing framework that allows for multiple debt issues. Since firms default on all of their obligations, total debt is instrumental in the likelihood of default and therefore in credit derivatives valuation. We use a single factor interest rate model where the exponential default frontier is based on total debt and is made coherent with observed bond prices. Analytical formulae are derived for credit default swaps, total return swaps (both fixed-for-fixed and fixed-for-floating), and credit risk options (CROs). Price behaviors and hedging properties of all these credit derivatives are investigated. Simulations document that credit derivatives prices may be significantly affected by terms of debt other than those of the reference obligation. The analysis of CROs indicates their superior ability to fine-tune the hedging of magnitude and arrival risks of default.     

Legal Restrictions in Personal Loan Markets

This study examines the pricing of personal loans in the form of second mortgages to determine whether state-specific default laws have an effect on the availability and cost of that debt. We examine the pricing of loans to higher risk borrowers and whether borrowers in states that limit lender ability to seek default remedies pay higher credit costs. Our results indicate that, for the most part, lenders rationally price loans to higher risk borrowers. However, when we focus on borrowers with low credit scores, the results indicate that mean actual loan rates are higher than those predicted by our model. The results also indicate that state-specific default laws have an effect on the price of credit. Finally, the results show that there is a greater degree of error in the pricing of second mortgage loans to borrowers with low credit scores than to borrowers with high credit scores.     

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.     

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.     

Municipal Bond Liquidity and Default Risk

This paper examines the pricing of municipal bonds. I use three distinct, complementary approaches to decompose municipal bond spreads into default and liquidity components, and find that default risk accounts for 74% to 84% of the average spread after adjusting for tax‐exempt status. The first approach estimates the liquidity component using transaction data, the second measures the default component with credit default swap data, and the third is a quasi‐natural experiment that estimates changes in default risk around pre‐refunding events. The price of default risk is high given the rare incidence of municipal default and implies a high risk premium.     

The rise of risk-based pricing of mortgage interest rates in Italy

This paper assesses how much mortgage interest rates in Italy are priced on credit risk as proxied by the probability of household mortgage delinquency estimated using the EU-Silc database. Owing to data availability, we restrict the analysis of mortgage pricing to Italian households. Consistent with the more widespread use of credit scoring, estimates indicate that Italian lenders have increasingly priced mortgage interest rates on household credit risk. For mortgages granted between 2000 and 2007, we find that a 1% point increase in the probability of default is associated with a 21 basis point rise in mortgage interest rates, lower than the 38 basis point premium Edelberg (2006) estimated for the US at the end of the 1990s.     

Financial statement comparability and credit risk

Prior research shows that firms’ financial statement comparability improves the accuracy of market participants’ valuation judgments and thus may reduce firms’ costs of capital. Distinct from prior research focusing on the equity market, we develop measures of comparability relevant to debt market participants based on the within-industry variability of Moody’s adjustments to reported accounting numbers for the purposes of credit rating. We examine two sets of adjustments: (1) to the interest coverage ratio and (2) to non-recurring income items. We validate these comparability measures by providing evidence that greater comparability is associated with lower frequency and magnitude of split ratings by credit rating agencies. We predict and find that greater comparability is associated with (1) lower estimated bid-ask spreads for traded bonds, (2) lower credit spreads for both bonds and five-year credit default swaps, and (3) a steeper one- to five-year credit default swap term structure. Our results are consistent with financial statement comparability reducing debt market participants’ uncertainty about and pricing of firms’ credit risk.