Pricing CDS spreads with Credit Valuation Adjustment using a mixture copula

Credit derivatives pricing models before Basel III ignored losses in market value stemming from higher probability of counterparty default. We propose a general credit derivatives pricing model to evaluate a Credit Default Swap (CDS) with counterparty risk, including the Credit Valuation Adjustment (CVA) in order to optimize the economic capital allocation. We work from the model proposed by Luciano (2003, Working Paper, International Center of Economic Research) and the general pricing representation established by Sorensen and Bollier (Financial Analysts Journal 1994;50(3):23–33) to provide a model close to the market practice, easy to implement and fitting with Basel III framework. We approach the dependence between counterparty risk and that of the reference entity with a technical tool: the copula, in particular, the mixture one that combines common “extreme” copulas. We study the CDS's vulnerability in extreme dependence cases. By varying Spearman's rho, the mixture copula covers a broad spectrum of dependence and ensures closed form prices. We end up with an application on real market data.     

Counterparty credit risk and the credit default swap market

Counterparty credit risk has become one of the highest-profile risks facing participants in the financial markets. Despite this, relatively little is known about how counterparty credit risk is actually priced. We examine this issue using an extensive proprietary data set of contemporaneous CDS transaction prices and quotes by 14 different CDS dealers selling credit protection on the same underlying firm. This unique cross-sectional data set allows us to identify directly how dealers' credit risk affects the prices of these controversial credit derivatives. We find that counterparty credit risk is priced in the CDS market. The magnitude of the effect, however, is vanishingly small and is consistent with a market structure in which participants require collateralization of swap liabilities by counterparties.     

A mathematical model for multi-name credit based on community flocking

We present a new mathematical model for multi-name credit that employs stochastic flocking. Flocking mechanisms have been used in a variety of models of biological, sociological and physical aggregation phenomena. As a direct application of a flocking mechanism, we introduce a credit risk model based on community flocking for a credit worthiness index. Correlations between different credit worthiness indices are explained in terms of communication rates and coupling strengths from the flocking system. Based on the flocking model, we compute credit curves for individual names and default time distributions. We also apply the proposed model to the pricing of credit derivatives such as credit default swaps and collateralized debt obligations.     

信用衍生品市场的国际经验与中国发展——基于金融结构和宏观稳定的分析

信用衍生品是国际资本市场上最具创新性的金融工具之一。发展信用衍生品市场不仅可以转移金融机构的信用风险,同时也可以缓解金融脱媒问题,防止资本市场快速膨胀、扭曲银行和金融体系。然而,信用衍生品也有其另一面。美国金融危机显示信用衍生品与金融结构具有复杂的联系机制,可能冲击宏观稳定。本文提出,我国应深入剖析美国的信用衍生品市场与金融结构关系,跟踪国际市场的改革和发展方向,探索符合国情的信用衍生品市场发展道路。     

Market Segmentation Effects in Corporate Credit Rating Changes: The Case of Emerging Markets

We examine stock market reactions to corporate credit rating changes in 26 emerging market countries included in the Morgan Stanley Capital International (MSCI) Emerging Market Index. We hypothesize and test the notion that emerging market firms in the American Depository Receipts (ADRs) markets are more likely to purchase ratings from the Big Two (Moody’s and S&P), and that they react more strongly to the announcements of corporate rating changes by Moody’s or S&P than to those of raters in local markets. We compare the effect of credit rating changes of the Big Two in two emerging stock markets: local markets (local currencies) and ADR markets (U.S. dollars). We find significant price reactions in the ADR markets, and insignificant reactions in local markets, and conclude that there is capital market segmentation in ADR markets for credit rating changes of emerging market firms. We find evidence that investors react more strongly in the ADR markets than local markets because they require higher costs of capital for firms cross-listed both in the ADR markets and local markets due to greater expected bankruptcy costs and foreign exchange risks of those firms. We also report that stock markets react significantly, not only to rating downgrades, but also to upgrades in the ADR markets.

Constant Proportion Debt Obligations (CPDOs): modeling and risk analysis

Constant Proportion Debt Obligations (CPDOs) are structured credit derivatives that generate high coupon payments by dynamically leveraging a position in an underlying portfolio of investment-grade index default swaps. CPDO coupons and principal notes received high initial credit ratings from the major rating agencies, based on complex models for the joint transition of ratings and spreads for all names in the underlying portfolio. We propose a parsimonious model for analysing the performance of CPDO strategies using a top-down approach that captures the essential risk factors of the CPDO. Our approach allows us to compute default probabilities, loss distributions and other tail risk measures for the CPDO strategy and analyse the dependence of these risk measures on various parameters describing the risk factors. We find that the probability of the CPDO defaulting on its coupon payments can be made arbitrarily small—and thus the credit rating arbitrarily high—by increasing leverage, but the ratings obtained strongly depend on assumptions on the credit environment (high spread or low spread). More importantly, CPDO loss distributions are found to exhibit a wide range of tail risk measures inside a given rating category, suggesting that credit ratings are insufficient performance indicators for such complex leveraged strategies. A worst-case scenario analysis indicates that CPDO strategies have a high exposure to persistent spread-widening scenarios and that CPDO ratings are shown to be quite unstable during the lifetime of the strategy.     

Information risk and credit contagion

This paper demonstrates a positive relationship between information risk and the credit contagion effect. We use abnormal changes in the Credit Default Swaps (CDS) spreads to measure the contagion effect, and the dispersion of analyst forecasts as a proxy for information risk. We find that firms with higher information risk suffer a greater contagion effect that occurs in advance to the credit default events. This finding is robust under controls of key firm-specific characteristics and general condition of stock and credit markets.     

The (un)informative value of credit rating announcements in small markets

This work examines the information value of local Israeli credit rating announcements. This matter is also important to other small markets, in which a debt issuer may take advantage of a “rating shopping” process or choose to avoid a rating procedure altogether, because the agencies do not carry out unsolicited rating. We analyze the bond and equity markets response to various rating announcements at different time periods. We find that except for downgrades in 2008–2009 the rating announcements have no information value. It seems that generally the market internalizes most of the information prior to the rating announcements.     

Market-specific and currency-specific risk during the global financial crisis: Evidence from the interbank markets in Tokyo and London

This paper investigates how international money markets reflected credit and liquidity risk during the global financial crisis. After matching the currency denomination, we examine how the Tokyo Interbank Offered Rate (TIBOR) was synchronized with the London Interbank Offered Rate (LIBOR). We find remarkably asymmetric responses in market-specific and currency-specific risk during the crisis. The regression results suggest that market-specific credit risk increased the difference across markets, whereas liquidity risk caused the difference across currency denominations. They also support the view that liquidity shortage of the US dollar occurred in international money markets during the crisis. Coordinated central bank liquidity provisions were useful in reducing the liquidity shortage of the US dollar, but their effectiveness was asymmetric across markets.     

Credit derivatives and loan pricing

This paper examines the relation between the new markets for credit default swaps (CDS) and banks’ pricing of syndicated loans to US corporates. We find that changes in CDS spreads have a significantly positive coefficient and explain about 25% of subsequent monthly changes in aggregate loan spreads during 2000–2005. Moreover, when compared to traditional explanatory factors, they turn out to be the dominant determinant of loan spreads. In particular, they explain loan rates much better than same rated bonds. This suggests that CDS prices contain, beyond general credit risk, to a substantial extent information relevant for bank lending. We also find that, over time, new information from CDS markets is faster incorporated into loans, but information from other markets is not. Overall, our results indicate that the markets for CDS have gained an important role for banks.     

Selecting credit rating models: a cross-validation-based comparison of discriminatory power

In commercial banking, various statistical models for corporate credit rating have been theoretically promoted and applied to bank-specific credit portfolios. In this paper, we empirically compare and test the performance of a wide range of parametric and nonparametric credit rating model approaches in a statistically coherent way, based on a ‘real-world’ data set. We repetitively (k times) split a large sample of industrial firms’ default data into disjoint training and validation subsamples. For all model types, we estimate k out-of-sample discriminatory power measures, allowing us to compare the models coherently. We observe that more complex and nonparametric approaches, such as random forest, neural networks, and generalized additive models, perform best in-sample. However, comparing k out-of-sample cross-validation results, these models overfit and lose some of their predictive power. Rather than improving discriminatory power, we perceive their major contribution to be their usefulness as diagnostic tools for the selection of rating factors and the development of simpler, parametric models.

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.      

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.     

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.     

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.     

Credit risk transfer and financial sector stability

In this paper, we study credit risk transfer (CRT) in an economy with endogenous financing (by both banks and non-bank institutions). Our analysis suggests that the incentive of banks to transfer credit risk is aligned with the regulatory objective of improving stability, and so the recent development of credit derivative instruments is to be welcomed. Moreover, we find the transfer of credit risk from banks to non-banks to be more beneficial than CRT within the banking sector. Intuitively, this is because it allows for the shedding of aggregate risk which must otherwise remain within the relatively more fragile banking sector. Therefore, regulators should act to maximize the benefits from CRT by encouraging the development of instruments favorable to the cross-sectoral transfer of aggregate credit risk (including basket credit derivatives such as collateralized debt obligations). Finally, we derive the optimal regulatory stance for banks relative to non-bank financial institutions. We show that a level playing field approach is sub-optimal. Regulatory stances should be set to actively encourage cross-sector CRT, first because of the higher fragility of the banking sector and second to induce banks to incur the costs of CRT which otherwise lead them to undertake an insufficient amount of CRT.     

How Much Do Banks Use Credit Derivatives to Hedge Loans?

Before the credit crisis that started in mid-2007, it was generally believed by top regulators that credit derivatives make banks sounder. In this paper, we investigate the validity of this view. We examine the use of credit derivatives by US bank holding companies with assets in excess of one billion dollars from 1999 to 2005. Using the Federal Reserve Bank of Chicago Bank Holding Company Database, we find that in 2005 the gross notional amount of credit derivatives held by banks exceeds the amount of loans on their books. Only 23 large banks out of 395 use credit derivatives and most of their derivatives positions are held for dealer activities rather than for hedging of loans. The net notional amount of credit derivatives used for hedging of loans in 2005 represents less than 2% of the total notional amount of credit derivatives held by banks and less than 2% of their loans. We conclude that the use of credit derivatives by banks to hedge loans is limited because of adverse selection and moral hazard problems and because of the inability of banks to use hedge accounting when hedging with credit derivatives. Our evidence raises important questions about the extent to which the use of credit derivatives makes banks sounder.

美国信用评级市场与监管变迁及其借鉴

美国信用评级业发展已经有上百年的历史。市场高度垄断、严重的"顺周期"现象、利益冲突、金融市场及监管当局对评级的严重依赖是当今美国信用评级市场存在的四大问题。目前美国信用评级业形成了以行业自律为基础、NRSRO注册与美国证券交易委员会(SEC)直接监管相结合的信用评级监管体系。美国信用评级市场发展及监管变迁对我国的启示是:应逐步打破国际评级市场完全由美国评级机构垄断的现有格局,必须逐步构建有中国自身特色的本土评级体系,并将本土评级体系的培育与国内债券市场建设、"走出去"战略及人民币国际化战略结合起来,降低国内监管部门及市场主体对外部评级机构的依赖。     

Laying off credit risk: Loan sales versus credit default swaps

How do markets for debt cash flow rights, with and without accompanying control rights, affect the efficiency of lending? A bank makes a loan, learns if it needs monitoring, and then decides whether to lay off credit risk. The bank can transfer credit risk by either selling the loan or buying a credit default swap (CDS). With a CDS, the originating bank retains the loan's control rights; with loan sales, control rights pass to the loan buyer. Credit risk transfer leads to excessive monitoring of riskier credits and insufficient monitoring of safer credits. Increases in banks' cost of equity capital exacerbate these effects. For riskier credits, loan sales typically dominate CDS but not for safer credits. Once repeated lending and consequent reputation concerns are modeled, although CDSs remain dominated by loan sales for riskier credits, for safer credits they can dominate loan sales, supporting better monitoring (albeit to a limited extent) while allowing efficient risk sharing. Restrictions on the bank's ability to sell the loan expand the range in which CDSs are used and monitoring is too low.