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Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation

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  • Peter Carr
  • Liuren Wu

Abstract

We propose a dynamically consistent framework that allows joint valuation and estimation of stock options and credit default swaps written on the same reference company. We model default as controlled by a Cox process with a stochastic arrival rate. When default occurs, the stock price drops to zero. Prior to default, the stock price follows a jump-diffusion process with stochastic volatility. The instantaneous default rate and variance rate follow a bivariate continuous process, with its joint dynamics specified to capture the observed behavior of stock option prices and credit default swap spreads. Under this joint specification, we propose a tractable valuation methodology for stock options and credit default swaps. We estimate the joint risk dynamics using data from both markets for eight companies that span five sectors and six major credit rating classes from B to AAA. The estimation highlights the interaction between market risk (return variance) and credit risk (default arrival) in pricing stock options and credit default swaps. Copyright The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oupjournals.org, Oxford University Press.

Suggested Citation

  • Peter Carr & Liuren Wu, 2010. "Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(4), pages 409-449, Fall.
  • Handle: RePEc:oup:jfinec:v:8:y:2010:i:4:p:409-449
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbp010
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    Cited by:

    1. Olena Burkovska & Maximilian Ga{ss} & Kathrin Glau & Mirco Mahlstedt & Wim Schoutens & Barbara Wohlmuth, 2016. "Calibration to American Options: Numerical Investigation of the de-Americanization," Papers 1611.06181, arXiv.org.
    2. Thaddeus Neururer & George Papadakis & Edward J. Riedl, 2016. "Tests of investor learning models using earnings innovations and implied volatilities," Review of Accounting Studies, Springer, vol. 21(2), pages 400-437, June.
    3. Deepa Dhume Datta & Juan M. Londono & Bo Sun & Daniel O. Beltran & Thiago Revil T. Ferreira & Matteo Iacoviello & Mohammad Jahan-Parvar & Canlin Li & Marius del Giudice Rodriguez & John H. Rogers, 2017. "Taxonomy of Global Risk, Uncertainty, and Volatility Measures," International Finance Discussion Papers 1216, Board of Governors of the Federal Reserve System (U.S.).
    4. repec:eee:finlet:v:23:y:2017:i:c:p:306-313 is not listed on IDEAS
    5. Reindl, Johann & Stoughton, Neal & Zechner, Josef, 2013. "Market implied costs of bankruptcy," CFS Working Paper Series 2013/27, Center for Financial Studies (CFS).
    6. Jan Hanousek & Evzen Kocenda & Jan Novotny, 2014. "Price jumps on European stock markets," Borsa Istanbul Review, Research and Business Development Department, Borsa Istanbul, vol. 14(1), pages 10-22, March.
    7. Benjamin Yibin Zhang & Hao Zhou & Haibin Zhu, 2009. "Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms," Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5099-5131, December.
    8. Da Fonseca, José & Gottschalk, Katrin, 2014. "Cross-hedging strategies between CDS spreads and option volatility during crises," Journal of International Money and Finance, Elsevier, vol. 49(PB), pages 386-400.
    9. Hanousek Jan & Kočenda Evžen & Novotný Jan, 2012. "The identification of price jumps," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 53-77, January.
    10. Carr, Peter & Wu, Liuren, 2016. "Analyzing volatility risk and risk premium in option contracts: A new theory," Journal of Financial Economics, Elsevier, vol. 120(1), pages 1-20.
    11. Igor V. Kravchenko & Vladislav V. Kravchenko & Sergii M. Torba & Jos'e Carlos Dias, 2017. "Pricing double barrier options on homogeneous diffusions: a Neumann series of Bessel functions representation," Papers 1712.08247, arXiv.org.
    12. Hao Wang & Hao Zhou & Yi Zhou, 2011. "Credit default swap spreads and variance risk premia," Finance and Economics Discussion Series 2011-02, Board of Governors of the Federal Reserve System (U.S.).
    13. Da Fonseca, José & Ignatieva, Katja & Ziveyi, Jonathan, 2016. "Explaining credit default swap spreads by means of realized jumps and volatilities in the energy market," Energy Economics, Elsevier, vol. 56(C), pages 215-228.
    14. Augustin, Patrick & Subrahmanyam, Marti G. & Tang, Dragon Yongjun & Wang, Sarah Qian, 2014. "Credit Default Swaps: A Survey," Foundations and Trends(R) in Finance, now publishers, vol. 9(1-2), pages 1-196, December.
    15. Jan Novotn?? & Jan Hanousek & Ev??en Ko??enda, 2013. "Price Jump Indicators: Stock Market Empirics During the Crisis," William Davidson Institute Working Papers Series wp1050, William Davidson Institute at the University of Michigan.
    16. Wang, Hao & Zhou, Hao & Zhou, Yi, 2013. "Credit default swap spreads and variance risk premia," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3733-3746.
    17. Claudio Fontana & Juan Miguel A. Montes, 2012. "A unified approach to pricing and risk management of equity and credit risk," Papers 1212.5395, arXiv.org, revised May 2013.
    18. Azusa Takeyama & Nick Constantinou & Dmitri Vinogradov, 2012. "Credit Risk Contagion and the Global Financial Crisis," IMES Discussion Paper Series 12-E-15, Institute for Monetary and Economic Studies, Bank of Japan.
    19. Azusa Takeyama & Nick Constantinou & Dmitri Vinogradov, 2012. "A Framework for Extracting the Probability of Default from Stock Option Prices," IMES Discussion Paper Series 12-E-14, Institute for Monetary and Economic Studies, Bank of Japan.
    20. Jan Hanousek & Evžen Kočenda & Jan Novotný, 2016. "Shluková analýza skoků na kapitálových trzích
      [Cluster Analysis of Jumps on Capital Markets]
      ," Politická ekonomie, University of Economics, Prague, vol. 2016(2), pages 127-144.
    21. Michele Bianchi & Frank Fabozzi, 2015. "Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 243-273, August.
    22. Câmara, António & Popova, Ivilina & Simkins, Betty, 2012. "A comparative study of the probability of default for global financial firms," Journal of Banking & Finance, Elsevier, vol. 36(3), pages 717-732.
    23. Agostino Capponi & Stefano Pagliarani & Tiziano Vargiolu, 2014. "Pricing vulnerable claims in a Lévy-driven model," Finance and Stochastics, Springer, vol. 18(4), pages 755-789, October.
    24. repec:eee:ecmode:v:64:y:2017:i:c:p:48-59 is not listed on IDEAS

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