CreditGrades Model Research Articles

Stock Prices and Stock Return Volatilities Impliedby the Credit Market

In this article, the author compares equity and credit investors’ opinions on price formation in the equity market. More exactly, he inverts the CreditGrades model in order to back out credit-implied stock prices and stock return volatilities from credit default swap spreads for companies in the DJIA index. The credit-implied stock prices often deviate significantly from actual stock prices over the long term. Meanwhile, their day-to-day movements are significantly correlated with actual stock returns for most firms in the DJIA. In an attempt to demonstrate potential applications of credit-implied stock prices, the author constructs simple “capital structure arbitrage” trading strategies based on past credit-implied prices. These strategies only require the buying and selling of stocks and differ from traditional cross-capital structure strategies by being suitable for retail investors and other investors without access to the credit derivatives market. The credit-implied volatilities, in turn, behave rather similarly to observed stock market volatilities but without any ghost effects. The author demonstrates how an alternative credit-based “fear gauge,” comparable to the CBOE VIX but emanating from the credit market, can be constructed using the credit-implied volatilities. He calls this implied volatility index the Credit-Implied Volatility Index (CIVX). Finally, a plot of the entire term structure of implied volatilities demonstrates a distinct maturity volatility skew.

Stock Prices and Stock Return Volatilities Implied by the Credit Market

In this paper we compare equity- and credit investors’ opinions on the price formation in the equity market. More exactly, we invert the CreditGrades model in order to back out credit-implied stock prices and stock return volatilities from credit default swap spreads for the firms in the DJIA index. The creditimplied stock prices often deviate significantly from actual stock prices over the longer term. Meanwhile, their day-to-day movements are significantly correlated with actual stock returns for most firms in the DJIA index. In an attempt to demonstrate potential applications of credit-implied stock prices we construct simple “capital structure arbitrage” trading strategies based on past credit-implied prices. Our strategies only require the buying and selling of stocks and differ from traditional cross-capital structure strategies by being suitable for retail investors and other investors without access to the credit derivatives market. The credit-implied volatilities, in turn, behave rather similarly to observed stock market volatilities but without any ghost effects. We demonstrate how an alternative credit-based “fear gauge”, comparable to the VIX index but emanating from the credit market, can be constructed using the credit-implied volatilities. We call this implied volatility index the Credit-Implied Volatility Index (CIVX) index. Finally, a plot of the entire term-structure of implied volatilities demonstrates a distinct maturity volatility skew.

Combining hazard rates with the CreditGrades model: A hybrid method to value CDS contracts

In this paper, we propose a hybrid method that combines a hazard rate model with the CreditGrades model to value credit default swap (CDS) contracts. The CreditGrades model is considered an industry benchmark for analyzing credit derivatives. The hybrid method makes use of the default probability generated by the CreditGrades model to determine the hazard rate specific to the bond issuing firm. In this way, the hybrid method is empirically shown to produce better CDS forecast.

The relationship between credit default swap spreads and equity prices

To meet new Basel III capital requirements, banks have to proxy unobserved credit default swap (CDS) time series for their over-the-counter derivative counterparties to determine the credit valuation adjustment (CVA) value-at-risk. This paper establishes a link between returns on CDSs and corresponding equity prices that allows CDS proxy series to be generated that retain important idiosyncratic risk, which is lost in more typical mapping methods. In so doing, the multifactor model developed shows a consistent pricing of credit risk in both the CDS market and the equity market. The model is intuitive, requires few assumptions and relies on readily available data. The model also performs well when compared with the CreditGrades model for proxy CDS spreads. Therefore, it tackles the modeling challenges set by Basel III for proxying single-name CDS spreads.

Evaluation of conducting capital structure arbitrage using the multi-period extended Geske–Johnson model

This study utilizes a multi-period structural model developed by Chen and Yeh (Pricing credit default swaps with the extended Geske–Johnson Model. Working paper, 2006), which extends the Geske and Johnson (J Financ Quant Anal 19:231–232, 1984) compound option model to evaluate the performance of capital structure arbitrage. In the paper, first of all, we predict the default probability for each firm using the multi-period Geske–Johnson model that assumes endogenous default barriers. Second, based on the arbitrage performance of 369 North American obligators from 2004 to 2008, we find that the extended Geske–Johnson model is more suitable than the CreditGrades model for exploiting the mispricing between equity prices and credit default swap spreads. Finally, the Geske–Johnson model also performs well in extreme market condition, such as the financial crisis around 2008.

CreditGrades Framework within Stochastic Covariance Models

In this paper we study a multivariate extension of a structural credit risk model, the CreditGrades model, under the assumption of stochastic volatility and correlation between the assets of the companies. The covariance of the assets follows two popular models which are non-overlapping extensions of the CIR model to dimensions greater than one, the Wishart process and the Principal component process. Under CreditGrades, we find quasi closed-form solutions for equity options, marginal probabilities of defaults, and some other major financial derivatives.

Pricing Credit Default Swaps with Option-Implied Volatility

Using the industry benchmark CreditGrades model to analyze credit default swap (CDS) spreads across a large number of companies during the 2007–09 credit crisis, the authors demonstrate that the performance of the model can be significantly improved by calibrating it with option-implied volatility rather than with historical volatility. Moreover, the advantage of using option-implied volatility is greater among companies with more volatile CDS spreads, more actively traded options, and lower credit ratings.

Capital Structure Arbitrage: An Analysis of the Australian CDS Market

This study investigates the ability of the CreditGrades model to estimate Credit Default Swap (CDS) spreads by comparing the difference between model and market spreads using a number of volatility inputs. We then develop a convergence style capital structure arbitrage trading strategy and test its profitability in the Australian CDS market before and during the financial crisis. We conclude that model performance before the crisis is consistent with previous literature, yet model and market spreads diverge considerably throughout the more volatile period. Although forward-looking option-implied volatility inputs produce inferior fit compared to long-term historical volatility inputs, they are more correlated with medium term changes in market spreads, and thus significantly more profitable within the trading strategy during the volatile period. While trades using all volatility inputs are highly risky at both the individual obligator and the iTraxx Australia Index level, those based on implied volatility are found to be highly profitable, on average, after transaction costs are taken into account. The strategy is significantly less risky when positions are combined into an equally weighted index of arbitrage trades. Financial firms, with which structural models have traditionally struggled, are included in the sample by way of a model calibration procedure, and their inclusion does not decrease the accuracy of the model, nor the profitability of the trading strategy.

An extension of CreditGrades model approach with Lévy processes

This paper proposes an extended CreditGrades model called the Lévy CreditGrades model, which is driven by a Lévy process. In this setting, quasi closed-form formulae for pricing equity options to a reference firm and for calculating its survival probabilities are derived. Moreover, using three tractable Lévy CreditGrades models, we compute implied volatilities on equity options and term structures of credit default swaps (CDSs) and we examine the jump risk effects of the firm's asset value on short term CDS spreads and equity volatility skew. As a result, with this extension, our model is found to have more significant abilities than the original model introduced by Finger et al. [CreditGrades Technical Document, RiskMetrics Group, 2002] and Stamicar and Finger [J. Credit Risk, 2006, 2(1), 1–20], and it is more appropriate for pricing both equity and credit derivatives simultaneously.

A note on the survival probability in CreditGrades

This paper examines survival probability in the CreditGrades model. We find that the exact closed-form formula stated in Finger et al (2002) for the survival probability of a firm is incorrect. We correct the formula and compare the exact survival probability with the frequently used approximation. We find that there are circumstances in which these two formulas differ significantly. This is in particular the case if one considers highly leveraged companies such as banks.

How Efficient are Credit Default Swap Markets? An Empirical Study of Capital Structure Arbitrage Based on Structural Pricing Models

We investigate the efficiency of the credit default swap (CDS) market via the profitability and risk of capital structure arbitrage strategies based on observed mispricing in the CDS market over the years 2002 to 2006. We find that the CDS market has been inefficient in our observation period although this inefficiency declined over time. For this purpose, we calculate CDS premiums by means of the CreditGrades (2002) model and the models of Leland and Toft (1996) and Zhou (2001) and apply those within a capital structure arbitrage context for a dataset covering more than 800,000 observations. Our results indicate that structural credit risk models can adequately replicate market spreads but still produce significant positive arbitrage returns within our strategy. This also holds when transaction costs are incorporated. Accounting for risk via the Sharpe ratio reveals that the CDS market was inefficient at the beginning of our sample period but became efficient in the years 2004/2005 consistent with soaring trading volumes and the introduction of CDS index trading at this time. We are also able to show that the mathematically more advanced Leland and Toft and Zhou models provide larger arbitrage returns within our strategy. Considering rating classes, the arbitrage returns increase as obligors become riskier, in line with standard investment theory.

CreditGrades and the iTraxx CDS Index Market

In the study reported, the CreditGrades model was used to calculate credit default swap spreads and the spreads were compared with empirically observed CDS spreads for eight iTraxx indices covering Europe. Theoretical and empirical spread changes were found to be significantly correlated. Also, lagged theoretical spread changes were correlated with current iTraxx spread changes. The correlations indicate a close relationship between the stock market and the CDS market and also indicate some predictive ability of the CreditGrades model. Simple trading strategies based on the autocorrelation and predictive ability of the model produced positive profits, before trading costs, when trading was within the bid–ask spread.

Incorporating equity derivatives into the CreditGrades model

In this paper we extend the CreditGrades structural model to include implied volatilities. Analytical formulas that include both asset volatility and leverage are derived for European puts and calls. Incorporating implied volatilities provides an alternative to standard implementations of structural models where asset volatilities are obtained from historical equity volatilities. This is particularly useful as a credit warning signal since we expect implied volatilities to spike during a credit crisis. In addition, implied volatilities can be used to infer not only asset volatility but also leverage. This is helpful when financial data do not accurately reflect the firm’s true leverage levels (such as companies with a large percentage of secured debt) or for firms whose leverages are difficult to estimate.