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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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.
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.
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).
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.
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.
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.
Granger causality test remains a popular method for causality analysis in time series due to its computational simplicity.
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.
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.
Series with a unit root is said to be integrated of order one, or I(1).
Threshold cointegration allows for regime shift that could occur in the intercept, trend or the entire cointegration vector.
The Johansen tests of cointegration are likelihood-ratio tests.
See Dwyer (2015). The Johansen Tests for Cointegration, available at http://www.jerrydwyer.com/pdf/Clemson/Cointegration.pdf, accessed July 24, 2016.
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.
For more information about R package, refer to https://cran.r-project.org/web/packages/tsDyn/tsDyn.pdf. 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.
For more information, refer to Markit iTraxx Europe series 24 at: https://www.markit.com/NewsInformation/NewsAnnouncementsFile?CMSID=6eeeb28203e94f3f83c83d2a58609ab3.
For more details about R package named “urca”, refer to https://cran.r-project.org/web/packages/urca/urca.pdf, Accessed July 13, 2016.
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 https://sccn.ucsd.edu/wiki/Chapter_3.5._Model_order_selection.
Both TVAR.LR test and TVECM.HS test are available in R package tsDyn; for more information, refer to https://cran.r-project.org/web/packages/tsDyn/tsDyn.pdf; accessed at July 13, 2016.
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.
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.
Andersen T, Bondarenko O (2007) Construction and Interpretation of Model-Free Implied Volatility. NBER Working Paper No. 13449
Balke N, Fomby T (1997) Threshold Cointegration. Research Paper. Federal Reserve Bank of Dallas. Available at http://dallasfed.org/assets/documents/research/papers/1992/wp9209.pdf
Black F, Cox J (1976) Valuing Corporate Securities: Some Effects of Bond Indenture Provisions. J Financ 31(2):351–367
Black F, Scholes M (1973) The Pricing of Options and Corporate Liabilities. J Polit Econ 81(3):637–654
Blair BJ, Poon S-H, Taylor SJ (2001) Forecasting S&P 100 Volatility: The Incremental Information Content of Implied Volatilities and High-Frequency Index Returns. J Econ 105:5–26
Blanco R, Brenan S, Marsh I (2005) An Empirical Analysis of the Dynamic Relation between Investment-Grade Bonds and Credit Default Swaps. J Financ 60(5):2255–2281
Chan-Lau J A, Kim YS (2004) Equity Prices, Credit Default Swaps, and Bond Spreads in Emerging Markets, IMF Working Paper, No. WP/04/27
Collin-Dufresne P, Goldstein RS, Martin JS (2001) The Determinants of Credit Spread Changes. J Financ 56(6):2177–2208
Corzo M T, Gomez-Biscarri J, Lazcano L (2012) The Co-Movement of Sovereign Credit Default Swaps and Bonds, and Stock Markets in Europe. Available at SSRN: http://ssrn.com/abstract=2000057 or doi:10.2139/ssrn.2000057
Crouch P, Marsh, I (2005) Arbitrage Relationships and Price Discovery in the Autos Sector of the Credit Market. Working Paper Series, Cass Business School
Delianedis G, Geske R (2001) The Components of Corporate Credit Spreads: Default, Recovery, Tax, Jumps, Liquidity, and Market Factors. Working paper 22–01, UCLA Anderson, School of Management
Demeterfi K, Derman E, Kamal M, Zhou J (1999) More Than You Ever Wanted to Know About Volatility Swaps. Goldman Sachs Quantitative Strategies Research Notes
Du L, Masli A, Meschke F (2013) The Effect of Credit Default Swaps on the Pricing of Audit Services. Working Paper Series, School of Business, The University of Kansas
Duffi D, Singleton K (1999) Modelling Term Structures of Defaultable Bonds. Rev Financ Stud 12(4):687–720
Dwyer GP (2015) The Johansen Tests for Cointegration. Available at http://www.jerrydwyer.com/pdf/Clemson/Cointegration.pdf. Accessed July 24, 2016
Enders W (2004) Applied Econometric Time Series (Second ed.). John Wiley & Sons, Hoboken
Eyssell T, Fund H-G, Zhang G (2013) Determinants and Price Discovery of China Sovereign Credit Default Swaps. China Econ Rev 24(C):1–15
Fabozzi FJ, Cheng X, Chen R-R (2007) Exploring the Components of Credit Risk in Credit Default Swaps. Finance Research Letters 4:10–18
Figuerola-Ferretti I, Paraskevopoulos I (2010) Pairing Market Risk and Credit Risk, Working paper. Carlos III University, Madrid
Fontana A, Scheicher M (2010) An Analysis of Euro Area Sovereign CDS and Their Relation with Government Bonds. European Central Bank, Working Paper Series, No. 1271
Forte S, Lovreta L (2008) Credit Risk Discovery in the Stock and CDS Market: Who, When and Why Leads? Available at http://www.finance-innovation.org/risk09/work/1166347.pdf
Fung H-G, Sierra G, Yau J, Zhang, G (2008) Are the U.S. Stock Market and Credit Default Swap Market Related? Evidence from the CDX Indices. Available at http://www.umsl.edu/divisions/business/files/pdfs/Zhang_Publication/CDS%20JAI%20Final%20FSYZ.pdf
Granger C (1981) Some Properties of Time Series Data and Their Use in Econometric Model Specification. J Econ 16(1):121–130
Greatrex CA (2009) Credit Default Swap Market Determinants. The Journal of Fixed Income 18:18–32
Gregory A, Hansen B (1996) Residual-Based Tests for Cointegration in Models with Regime Shifts. Journal of Econometrics 70: 99–126, available at http://www.ssc.wisc.edu/~bhansen/papers/joe_96.pdf. Accessed 24 Jul 2016
Grouard M H, Lévy S, Lubochinsky C (2003) Stock Market Volatility: From Empirical Data to Their Interpretation. Working Paper, FSR, Banque de France
Hansen B (1999) Threshold Effects in Non-Dynamic Panels: Estimation, Testing, and Inference. Journal of Econometrics 93: 345–368. Available at ftp://ftp.soc.uoc.gr/students/aslanidis/My%20documents/papers/Hansen%20(1999).pdf. Accessed 24 Jul 2016
Hansen B, Seo B (2002) Testing for Two-Regime Threshold Cointegration in Vector Error-Correction Models. Journal of Econometrics 110: 293–318. Available at http://www.ssc.wisc.edu/~bhansen/papers/joe_02.pdf. Accessed 24 Jul 2016
Hull J, White A (2000) Valuing Credit Default Swaps I: No counterparty Default Risk. J Deriv 8(1):29–40
Jacobs M, Karagozoglu A, Peluso, C (2010) Measuring Credit Risk: CDS Spreads vs. Credit Ratings. Available at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.455.8017&rep=rep1&type=pdf. Accessed 19 Aug 2016
Jarrow R, Turnbull S (1995) Pricing Derivatives on Financial Securities Subject to Default Risk. J Financ 50(1):53–85
Jiang G, Tian Y (2003) Model-Free Implied Volatility and Its Information Content. Available at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.194.7470&rep=rep1&type=pdf. Accessed 19 Aug 2016
Johansen S (1998) Statistical Analysis of Cointegration Vectors. J Econ Dyn Control 12(2–3):231–254
Kapar B, Olmo J (2011) The Determinants of Credit Default Swap Spreads in the Presence of Structural Breaks and Counterparty Risk. Working Paper 2011/02, Department of Economics, City University, London
Lee V, Fang V, Lin E (2007) Volatility Linkages and Spillovers in Stock and Bond Markets: Some International Evidence. Journal of International Finance and Economics 7(1):1–10
Litterman R, Iben T (1991) Corporate Bond Valuation and the Term Structure of Credit Spreads. J Portf Manag 17(3):52–64
Lo M, Zivot E (2001) Threshold Cointegration and Nonlinear Adjustment to the Law of One Price. Macroecon Dyn 5:533–576
Longstaff FA, Mithal S, Neis E (2005) Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from The Credit Default Swap Market. J Financ 60(5):2213–2253
Longstaff FA, Pan J, Pedersen LH, Singleton KJ (2007) How Sovereign is Sovereign Credit Risk? Unpublished Working Paper, UCLA Anderson School, MIT Sloan School, NYU Stern School, and Stanford Graduate School of Business
Merton R (1974) On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. J Financ 29(2):449–470
Mayhew S, Stivers C (2003) Stock Return Dynamics, Option Volume, and the Information Content of Implied Volatility. J Futur Mark 23(7):615–646
Ngene G (2012) Momentum, Nonlinear Price Discovery and Asymmetric Spillover: Sovereign Credit Risk and Equity Markets of Emerging Countries. Available at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.455.8225&rep=rep1&type=pdf. Accessed 19 Aug 2016
Ngene G, Hassan K (2012) Momentum, Nonlinearity in Cointegration and Price Discovery: Evidence from Sovereign CDS and Equity Markets of Emerging Countries. Available at http://cbt2.nsuok.edu/kwok/conference/submissions/swfa2013_submission_200.pdf
Norden L, Weber M (2009) The Co-movement of Credit Default Swap, Bond and Stock Markets: An Empirical Analysis. Eur Financ Manag 15(3):477–691
Otker-Robe I, Podpiera J (2010) The Fundamental Determinants of Credit Default Risk for European Large Complex Financial Institutions. IMF Working Paper, WP /10/153
Pan J, Singleton JK (2007) Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads. J Financ 63:2345–2384
Perron P (1989) The Great Crash, The Oil Price Shock, and The Unit Root Hypothesis. Econometrica 57:361–1401
Rapsomanikis G, Hallam D (2006) Threshold Cointegration in The Sugarethanol-Oil Price System in Brazil: Evidence from Nonlinear Vector Error Correction Models. Working Paper No. 22, FAO Commodity and Trade Policy Research
Schueler M (2001) CDS Basis Trading. Working Paper, JP Morgan Credit Derivatives Marketing
Schneider PG, Sögner L, Veza T (2007) The Economic Role of Jumps and Recovery Rates in the Market for Corporate Default Risk. Available at SSRN: http://ssrn.com/abstract=961341
Stigler M (2013) Threshold Cointegration: Overview and Implementation in R. 2010, revision 2013. Available at https://cran.r-project.org/web/packages/tsDyn/vignettes/ThCointOverview.pdf. Accessed 24 Jul 2016
Tang DY, Yan H (2007) Liquidity, Liquidity Spillover and Credit Default Swap Spreads. AFA Annual Meeting Paper, Chicago
Wang H, Zhou H, Zhou Y (2011) Credit Default Swap Spreads and Variance Risk Premia. Finance and Economics Discussion Series. Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C.
Zhu H (2004) An Empirical Comparison of Credit Spreads Between the Bond Market and the Credit Default Swap Market. BIS Working Paper No. 160
Zivot E, Andrews D (1992) Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis. J Bus Econ Stat 10(3):251–270
Markit iTraxx Europe series 24. Available at https://www.markit.com/NewsInformation/NewsAnnouncementsFile?CMSID=6eeeb28203e94f3f83c83d2a58609ab3. Accessed 17 Aug 2016
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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). https://doi.org/10.1007/s12197-017-9423-9
- Credit default swap
- iTraxx index
- Structural breaks