Relation between Credit Default Swap Spreads and Stock Prices: A Non-linear Perspective


In this study, we investigate the relation between credit risk, as implied in the credit default swaps (CDS), and market prices of Markit iTraxx Europe index companies. To test the hypothesis of co-integration between CDS and stock prices, we apply linear and non-linear models that allow for structural breaks. Using Johansen trace test of cointegration for a set of 109 pairs of CDS and stock prices of the companies included in the index, over the period of January 2012 to January 2016, we find that at the 10% level of significance, the null hypothesis of no cointegration is rejected for 26 pairs. We extend our analysis by allowing for a one-time structural break with unknown timing. Using alternative cointegration tests, we find that CDS and stock prices are cointegrated. More specifically, there are 47 companies in our sample for which CDS spreads and stock prices are cointegrated at the 10% level of significance. The existence of a long-run relation between CDS and stock prices of the European investment-grade companies is evidence for a possible transmission of shocks between the two segments of the financial market – the credit market (via CDS) and the stock market.

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  1. 1.

    According to Rapsomanikis and Hallam (2006), thresholds are considered as function of transaction and adjustment costs, or economic risk that prevents agents from adjusting continuously to changes in markets, as reflected by the linear cointegration.

  2. 2.

    The Markit iTraxx Europe index consists entirely of investment-grade companies; the Markit iTraxx Europe Crossover index includes sub-investment grade companies, but the stock market liquidity of these companies is very low which makes them inappropriate for our analysis.

  3. 3.

    On the other hand, unlike bonds, CDS contracts are standardized. Additionally, the lack of an up-front payment in CDS allows the credit risk to be traded separately from the underlying debt (Forte and Lovreta 2008).

  4. 4.

    There are basically two major types of models related to credit risk: structural models (Black and Scholes 1973; Merton 1974; Black and Cox 1976) that focus mainly on fundamental measures of financial strength of the issuers, and reduced-form models (Litterman and Iben 1991; Jarrow and Turnbull 1995; Duffie and Singleton 1999; Hull and White 2000), that focus on modelling credit risk as a statistical process rather than as a model of the firm’s capital structure. Figuerola-Ferretti and Paraskevopoulos (2010) argue that the structural model framework assumes the stock market is efficient, while reduced-form model relies on the debt market as the main source of credit risk information.

  5. 5.

    On September 22, 2003 CBOE together with Goldman Sachs updated its VIX methodology. The key change is that the new VIX no longer relies on the Black-Scholes (1973) model; instead, it is based on the concept of fair value of future variance developed by Demeterfi et al. (1999), and is calculated directly from prices of out-of-the-money call and put options independent of any model, i.e. the new volatility index is model-free.

  6. 6.

    iTraxx is the brand name for the family of CDS index products covering regions such as Europe, Australia, Japan and non-Japan Asia. iTraxx Europe is the most widely traded index and is composed of the most liquid 125 CDS referencing European investment-grade companies in six sectors: Autos, Consumers, Energy, Financials, Industrials, and TMT. It is the main reference of European credit index.

  7. 7.

    Granger causality test remains a popular method for causality analysis in time series due to its computational simplicity.

  8. 8.

    Price discovery as defined by these authors, is the process of uncovering the asset’s full information or permanent value. The unobservable permanent price reflects the fundamental value of the underlying asset.

  9. 9.

    The study explains that if the VIX and iTraxx CDS are cointegrated, price discovery may be regarded as a dynamic process in search for an equilibrium. This requires sudden adjustment of both indexes to new equilibrium for a given arrival of new information. If both markets do not react to new information in the same manner, one may lead the other. When such a lead-lag relationship appears, the leading market is said to provide price discovery.

  10. 10.

    Series with a unit root is said to be integrated of order one, or I(1).

  11. 11.

    Threshold cointegration allows for regime shift that could occur in the intercept, trend or the entire cointegration vector.

  12. 12.

    The Johansen tests of cointegration are likelihood-ratio tests.

  13. 13.

    See Dwyer (2015). The Johansen Tests for Cointegration, available at, accessed July 24, 2016.

  14. 14.

    The following TVAR tests can be used: 1) Test 1 vs. 2 that tests linear VAR vs. 1-threshold TVAR, 2) Test 1 vs. 3 that tests linear VAR vs. 2-threshold TVAR, and 3) Test 2 vs. 3 that tests 1-threshold TVAR vs. 2-threshold TVAR.

  15. 15.

    For more information about R package, refer to The Lagrange Multiplier (LM) test statistics in the Hansen and Seo test included in the tsDyn package (TVECM.HStest) is different from the LM statistic in the original work of Hansen and Seo (2002) but may be equal under some conditions.

  16. 16.

    For more information, refer to Markit iTraxx Europe series 24 at:

  17. 17.

    For more details about R package named “urca”, refer to, Accessed July 13, 2016.

  18. 18.

    Respectively, Akaike Information Criterion (AIC), Schwarz-Bayes Criterion (SBC) – also known as the Bayesian Information Criterion (BIC), Hannan-Quinn Criterion (HQ), and Akaike’s Final Prediction Error Criterion (FPE). In brief, each criterion is a sum of two terms, one that characterizes the entropy rate or prediction error of the model, and a second term that characterizes the number of freely estimated parameters in the model (which increases with increasing the model order). By minimizing both terms, we seek to identify a model that is parsimonious (does not overfit the data with too many parameters) and accurately modeling the data. For more information, refer to

  19. 19.

    Both TVAR.LR test and TVECM.HS test are available in R package tsDyn; for more information, refer to; accessed at July 13, 2016.

  20. 20.

    These are the following iTraxx companies: Anglo American, Astra Zeneca, BMW, Compagnie de Saint Gobain, Koninklijke DSM, Lafargeholcim, Lanxess, PostNL, Rentokil Initial, Rolls-Royce Holdings, Siemens, Solvay, LVMH Moet Hennessy Louis Vuitton, BP, Electricite de France, Repsol, Statoil, Allianz, AXA, Bayerische Landesbank, BNP Paribas, Intesa Sanpaolo, Mediobanca Banca di Credito Finanziario, Societe Generale, RBS, BT, Telenor, Vivendi, Carrefour, Diageo, Kering, Koninklijke Ahold, Koninklijke Philips.

  21. 21.

    These are the following iTraxx companies: Volvo, Akzo Nobel, Anglo American, Bayer, BMW, Compagnie de Saint Gobain, Rolls-Royce Holdings, Volkswagen, LVMH Moet Hennessy Louis Vuitton, BP, E.ON, Engie, Repsol, Statoil, Veolia Environnement, Aegon, BNP Paribas, Intesa Sanpaolo, Mediobanca Banca di Credito Finanziario, BT Group, Publicis Groupe, Telefonaktiebolaget L M Ericsson, Vivendi, Diageo, Kering.


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Correspondence to Miroslav Mateev.

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Mateev, M., Marinova, E. Relation between Credit Default Swap Spreads and Stock Prices: A Non-linear Perspective. J Econ Finan 43, 1–26 (2019).

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  • Credit default swap
  • iTraxx index
  • Cointegration
  • Structural breaks
  • Threshold

JEL classification

  • C58
  • G10
  • G12