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 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.     

Foreign Currency Derivatives versus Foreign Currency Debt and the Hedging Premium

This paper compares the effect on firm value of different foreign currency (FC) financial hedging strategies identified by type of exposure (short‐ or long‐term) and type of instrument (forwards, options, swaps and foreign currency debt). We find that hedging instruments depend on the type of exposure. Short‐term instruments such as FC forwards and/or options are used to hedge short‐term exposure generated from export activity while FC debt and FC swaps into foreign currency (but not into domestic currency) are used to hedge long‐term exposure arising from assets located in foreign locations. Our results relating to the value effects of foreign currency hedging indicate that foreign currency derivatives use increases firm value but there is no hedging premium associated with foreign currency debt hedging, except when combined with foreign currency derivatives. Taken individually, FC swaps generate more value than short‐term derivatives.     

Distressed Debt Restructuring in the Presence of Credit Default Swaps

The availability of credit insurance via credit default swaps has been closely associated with the emergence of empty creditors. We empirically investigate this issue by looking at the debt restructurings (distressed exchanges and bankruptcy filings) of rated, nonfinancial U.S. companies over the period January 2007–June 2011. Using different proxies for the existence of insured creditors, we do not find evidence that the access to credit insurance favors bankruptcy over a debt workout. However, we document higher recovery prices following a distressed exchange in firms where empty creditors are more likely to emerge.     

Takeover risk and the correlation between stocks and bonds

Existing research suggests that, for a given firm, stock returns and bond prices are positively related, and this implies a negative relation between stock returns and bond spreads. In this paper, we show how takeover risk influences this relation. Bondholders of high-rated firms can suffer losses in a takeover, particularly if the takeover is largely funded with debt, resulting in a more positive (or less negative) correlation between stock returns and bond spread changes. Consistent with this notion and based on a large sample of data covering the period from 1980 to 2000, we find that high-rated firms which are likely to be taken over have a more positive correlation between stock returns and bond spread changes, while target firms with a poison put or an indebtedness covenant have a more negative correlation. Overall, our findings have implications for the pricing and hedging of bonds and default risk based financial products such as credit default swaps.     

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.     

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.     

Hedging of a credit default swaption in the CIR default intensity model

An important issue arising in the context of credit default swap (CDS) rates is the construction of an appropriate model in which a family of options written on credit default swaps, referred to hereafter as credit default swaptions, can be valued and hedged. The goal of this work is to exemplify the usefulness of some abstract hedging results, which were obtained previously by the authors, for the valuation and hedging of the credit default swaption in a particular hazard process setup, namely, the CIR default intensity model.     

Has the CDS market lowered the cost of corporate debt?

Many have claimed that credit default swaps (CDSs) have lowered the cost of debt financing to firms by creating new hedging opportunities and information for investors. This paper evaluates the impact that the onset of CDS trading has on the spreads that underlying firms pay to raise funding in the corporate bond and syndicated loan markets. Employing a range of methodologies, we fail to find evidence that the onset of CDS trading lowers the cost of debt financing for the average borrower. Further, we uncover economically significant adverse effects on risky and informationally opaque firms.     

Efficient hybrid methods for portfolio credit derivatives

In this paper we discuss the computation of basket credit default swaps and collateralized debt obligation squared transactions. We suggest two hybrid algorithms for these two portfolio credit derivatives. The method combines the analytic approximation to the loss distribution of conditionally independent heterogeneous portfolios with the Monte Carlo simulation. The efficiency and accuracy of the algorithms are illustrated with examples.     

Credit derivatives and stock return synchronicity

The role of credit default swaps (CDS) in the 2008 financial crisis has been widely debated among regulators, investors, and researchers. While CDS were blamed for destabilizing the financial system, they remain effective tools for hedging credit risk, especially for major banks, and produce positive informational externalities to market participants. This paper examines whether the introduction of CDS enhances the amount of firm-specific information impounded in stock prices. We use stock return synchronicity to measure the amount of firm-specific information reflected in stock prices, with more firm-specific information being associated with a lower level of synchronicity. We find that a firm’s stock return synchronicity decreases after the commencement of CDS trading. This finding is robust to different model specifications, synchronicity measures, and endogeneity controlling methodologies. Furthermore, the decrease in stock return synchronicity is more pronounced for CDS firms with higher credit risk. Overall, our evidence supports the positive role of CDS in improving informativeness of stock prices.     

美国次贷危机中的金融衍生品及其风险传递研究

美国次贷危机愈演愈烈已造成了全球金融危机,究其原因在于其中的金融衍生品运用与监管不当。本文对该危机中的主要金融衍生品一次级按揭贷款、按揭贷款抵押支持债券、资产支持债券型抵押债务权益、信用违约互换等及其风险传递机制进行了深入分析,探讨了其对我国金融创新的启示。     

Structural default model with mutual obligations

In this paper we consider mutual obligations in an interconnected bank system and analyze their impact on the joint and marginal survival probabilities for individual banks. We also calculate prices of the corresponding credit default swaps and first-to-default swaps. To make the role of mutual obligations more transparent, we develop a simple structural default model with banks’ assets driven by correlated multidimensional Brownian motion with drift. We calculate closed form expressions for many quantities of interest and use them for the efficient model calibration. We demonstrate that mutual obligations have noticeable impact on the system behavior.     

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.     

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.     

Currency-Induced Credit Risk in a Dollarized Economy

We analyze the effects of exchange rate fluctuations on corporate credit default in a dollarized economy. The application, before an exogenous exchange rate shock, of a new regulation concerning currency-induced credit risk (CICR) in the Peruvian banking system created natural conditions for a comparison between exposed and unexposed corporate borrowers. We use firm-level data to find that CICR and debt dollarization have opposite effects on credit risk. While CICR increases default, debt dollarization reduces it. Our results suggest that banks transfer exchange risk as a hedging mechanism by lending to such borrowers in dollars only.     

Derivatives: Understanding Their Usefulness and Their Role in the Financial Crisis

This article makes two main arguments that are intended to guide policymakers and regulators of financial markets: (1) when used properly, derivatives are enormously useful to companies in managing business risks; and (2) neither derivatives nor derivatives‐related products played significant roles in causing or exacerbating the financial crisis of 2007–2009. The author begins by illustrating the corporate use of derivatives with a detailed example of how a large brewer uses both exchange‐traded wheat futures and over‐the‐counter aluminum swaps to hedge the risks of higher wheat and aluminum prices. In the process, the value of much‐maligned OTC derivatives, and the role of financial intermediaries in facilitating their use, are clearly demonstrated. The second part of the article refutes the popular claims, widely expressed in the media and on Capitol Hill, that derivatives were at the heart of the financial crisis. Losses and failures during the crisis are shown to have resulted primarily from excessive non‐derivative leverage and from investments in non‐derivative mortgage products that fell dramatically in value. The only significant exception involved the insurance company AIG, whose failure and bailout are attributable not only to large losses on credit default swaps, but to comparable losses on non‐derivative mortgage products. Moreover, by the time AIG failed, many other large financial institutions had already either failed or experienced large losses. What's more, and all but forgotten during the controversy, some large banks were able to reduce risk by hedging with those derivatives.     

Will banning naked CDS impact bond prices?

We develop a tractable partial equilibrium model to analyze the impact on the bond market generated by a ban on naked credit default swaps (CDS). We demonstrate that such a ban will have a negligible impact on the borrowing costs if CDS speculators are risk averse and take positions which are small relatively to the amount of debt outstanding. We find that the ban only excludes from the market moderately pessimistic investors, and induces the most pessimistic to implement their strategy on the short side of the bond market. Despite the sovereign debtor benefits from the reduced yields on the issued bonds, he will suffer from a diminished borrowing capacity after the ban. Such findings suggest that regulators should consider other measures to reduce instability arising from excessive speculation in derivatives markets.     

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.     

A Simple Approach to Valuing Risky Fixed and Floating Rate Debt

We develop a simple approach to valuing risky corporate debt that incorporates both default and interest rate risk. We use this approach to derive simple closed-form valuation expressions for fixed and floating rate debt. The model provides a number of interesting new insights about pricing and hedging corporate debt securities. For example, we find that the correlation between default risk and the interest rate has a significant effect on the properties of the credit spread. Using Moody's corporate bond yield data, we find that credit spreads are negatively related to interest rates and that durations of risky bonds depend on the correlation with interest rates. This empirical evidence is consistent with the implications of the valuation model.