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A Linear and Nonlinear Review of the Arbitrage-Free Parity Theory for the CDS and Bond Markets

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Topics in Numerical Methods for Finance

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 19))

Abstract

The arbitrage-free parity theory states that there is equivalence between credit default swap (CDS) spreads and bond market spreads in equilibrium. We show that the testing of this theory through the application of linear Gaussian bivariate modeling will lead to misleading results for CDS and bond spreads, and that linear stochastic modeling is not appropriate for CDS spreads. We propose the nonlinear and nonparametric dynamic tools of cross recurrence plots and cross recurrence plot measures to evaluate the arbitrage-free parity theory. We conclude that convergence is nonmean reverting and varying through time and across countries. This finding refutes the arbitrage-free parity theory. We also conclude that the probability to arbitrage will be affected by country and time-specific factors such as the expectation for country-specific government intervention. We propose that this methodology could be used by policy markets to supervise arbitrage activity and to influence policy making.

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Notes

  1. 1.

    One small additional point is that in order to ensure the test has the nuisance parameter free property, that is, that the test can be applied to the residuals of a model, the residuals of the ARGARCH process are first standardized, and transformed into the logged squared residuals [15, 16].

  2. 2.

    Other measure of CRP can be found at www.recurrence-plot.tk/.

  3. 3.

    We would like to acknowledge the use of the CRP toolbox 5.5 in the estimation of the CRPs and the CRP measures. This software was kindly given to use by Dr. Norbert Marwan of Potsdam University, see www.recurrence-plot.tk. We would also like to thank Dr. Stefan Schinkel, Dr. Denis O’Hora, Professor Stefan Thurner, and the referee for their valuable guidance and comments.

References

  1. Mengle, D.: Credit Derivatives: An Overview. In 2007 Financial Markets Conference. Federal Reserve Bank of Atlanta: International Swaps and Derivatives Association (2007)

    Google Scholar 

  2. Hull, J.C.: Options, Futures and Other Derivatives. 7th edn. Pearson Prentice Hall, New Jersey (2008)

    Google Scholar 

  3. Hull, J. C., White, A.: Valuing credit default swaps II: modeling default correlations. J. Derivatives 8(3), 12–22 (2001)

    Article  Google Scholar 

  4. Fontana, A., Scheicher, M.: An analysis of the euro are sovereign CDS and their relation with government bonds. Working Paper Series, European Central Bank.(1271) (2010)

    Google Scholar 

  5. Duffie, D.: Presidential address: asset price dynamics with slow-moving capital. J. Finance 65, 1237–1267 (2010)

    Article  Google Scholar 

  6. Mitchell, M., Pulvino, T.: Arbitrage crashes and the speed of capital. Working Paper Series, Mimeo (2011)

    Google Scholar 

  7. Blanco, R., Brennan, S., Marsh, I.W.: An empirical analysis of the dynamic relation between investment-grade bonds and credit default swaps. J. Finance 60(5), 2255–2281 (2005)

    Article  Google Scholar 

  8. Haugh, D., Ollivaud, P., Turner, D.: What Drives Sovereign Risk Premiums? OECD Economics Department Working Papers(718) (2009)

    Google Scholar 

  9. Delis, M.D., Mylonidis, N.: The chicken or the egg? A note on the dynamic interrelation between government bond spreads and credit default swaps. Finance Res. Lett. In Press, Corrected Proof (2010)

    Google Scholar 

  10. Kantz, H., Schreiber, T.: Non Linear Time Series Analysis. 2nd edn. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  11. Patterson, K.: An Introduction to Applied Econometrics. MacMillan, London (2000)

    Google Scholar 

  12. Granger, C.W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37(3), 424–438 (1969)

    Article  MathSciNet  Google Scholar 

  13. Moloney, K., Raghavendra, S.: Testing for nonlinear dependence in the Credit Default Swap Market. Economics Research International (Article ID 708704):12 (2011)

    Google Scholar 

  14. Brock, W.A., Dechert, W.D., LeBaron, B., Scheinkman, J.: A Test for Independence Based on the Correlation Dimension. Working papers Wisconsin Madison - Social Systems (1995)

    Google Scholar 

  15. Caporale, G.M., Ntantamis, C., Pantelidis, T., Pittis, N.: The BDS test as a test for the adequacy of a GARCH(1,1) specification: a monte carlo study. J. Financial Econometr. 3, 282–309 (2005)

    Article  Google Scholar 

  16. de Lima, Pedro J.F.: On the robustness of nonlinearity tests to moment condition failure. J. Econometrics 76(1–2), 251–280 (1997)

    Google Scholar 

  17. Eckmann, J.P., Kamphorst S.O., Ruelle, D.: Recurrence plots of dynamical systems. Europhys. Lett. 4(9), 973–977 (1987)

    Article  Google Scholar 

  18. Zbilut, J.P., Giuliani, A., Webber, C.L.: Detecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification. Phys. Lett. A 246(1–2), 122–128 (1998)

    Article  Google Scholar 

  19. Sauer, T., Yorke, J.A., Casdagli, M.: Embedology. J. Stat. Phys. 65(3–4), 579–616 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  20. Takens, F.: Detecting strange attractors in turbulence. In: Rand, D., Young, L. (eds.) Dynamical Systems and Turbulence. Springer, Berlin (1981)

    Google Scholar 

  21. Kantz, H., Schreiber, T.: Non Linear Time Series Analysis, 2nd edn. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  22. Marwan, N.: Encounters With Neighbours-Current Developments of Concepts Based On Recurrence Plots And Their Applications: PhD Thesis, University of Potsdam (2003)

    Google Scholar 

  23. Webber, C.L., Zbilut, J.P.: Recurrence quantification analysis of nonlinear dynamical systems. In: Riley, M.A., Van Orden, G., Arlington, C. (eds.) VATutorials in Contemporary Nonlinear Methods for the Behavioural Sciences. National Science Foundation (2005)

    Google Scholar 

  24. Marwan, N.: How to avoid potential pitfalls in recurrence plot based data analysis. In eprint arXiv:1007.2215: ARXIV (2010)

    Google Scholar 

  25. Schinkel, S., Dimigen, O., Marwan, N.: Selection of recurrence threshold for signal detection. Eur. Phys. J. Spec. Top. 164, 45–53 (2008)

    Article  Google Scholar 

  26. Bastos, J.A., Caiado, J.: Recurrence quantification analysis of global stock markets. Phys. Stat. Mech. Appl. 390(7), 1315–1325 (2011)

    Article  Google Scholar 

  27. Zbilut, J.P., Zaldivar-Comenges, J.M., Strozzi, F.: Recurrence quantification based Liapunov exponents for monitoring divergence in experimental data. Phys. Lett. A 297(3–4), 173–181 (2002)

    Article  MATH  Google Scholar 

  28. Marwan, N.M., Romano, C., Thiel, M., Kurths, J.: Recurrence plots for the analysis of complex systems. Phys. Rep. 438(5–6), 237–329 (2007)

    Article  MathSciNet  Google Scholar 

  29. Eckmann, J.P., Kamphorst, S.O., Ruelle, D.: Recurrence plots of dynamical systems. Europhys. Lett. 4(9), 973–977 (1987)

    Article  Google Scholar 

  30. Sprott, J.C.: Chaos and Time Series Analysis. 2nd edn. Oxford University Press, Oxford (2004)

    Google Scholar 

  31. Zbilut, J.P., Webber Jr. C.L.: Embeddings and delays as derived from quantification of recurrence plots. Phys. Lett. A. 171(3–4), 199–203 (1992)

    Article  Google Scholar 

  32. Webber Jr, C.L., Zbilut, J.P.: Dynamical assessment of physiological systems and states using recurrence plots strategies. J. Appl. Physiol. 76(2), 965–973 (1994)

    Google Scholar 

  33. Crowley, P.M.: Analyzing convergence and synchronicity of business and growth cycles in the euro area using cross recurrence plots. Eur. Phys. J. Spec. Top. 164, 67–84 (2008)

    Article  Google Scholar 

  34. Marwan, N., Kurths, J.: Nonlinear analysis of bivariate data with cross recurrence plots. Phys. Lett. A 302(5–6), 299–307 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  35. Li, L., Mizrach, B.: Tail return analysis of Bear Stearns’ credit default swaps. Econ. Model. 27, 1529–1536 (2010)

    Article  Google Scholar 

  36. Bollerslev, T.: Generalized autoregressive conditional heteroskedasticity. J. Econometrics. 31, 307–327 (1986)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. J.E. Cairnes School of Business and Economics, National University of Ireland Galway, Galway, Ireland

    Kitty Moloney & Srinivas Raghavendra

Authors
  1. Kitty Moloney
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  2. Srinivas Raghavendra
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Correspondence to Kitty Moloney .

Editor information

Editors and Affiliations

  1. , Dublin City Univ. Business School, Dublin City University, Ballymun Rd, Dublin 9, Dublin 9, Ireland

    Mark Cummins

  2. , Kemmy Business School, University of Limerick, Limerick, Ireland

    Finbarr Murphy

  3. Inst. for Numerical Computat. & Analy., 7 - 9 Dame Court, Dublin 2, Dublin 2, Ireland

    John J.H. Miller

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Moloney, K., Raghavendra, S. (2012). A Linear and Nonlinear Review of the Arbitrage-Free Parity Theory for the CDS and Bond Markets. In: Cummins, M., Murphy, F., Miller, J. (eds) Topics in Numerical Methods for Finance. Springer Proceedings in Mathematics & Statistics, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-3433-7_10

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