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A Framework for Extracting the Probability of Default from Stock Option Prices

  • Azusa Takeyama

    (Deputy Director and Economist, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: azusa.takeyama@boj.or.jp))

  • Nick Constantinou

    (Lectuer, Essex Business School, University of Essex (E-mail: nconst@essex.ac.uk))

  • Dmitri Vinogradov

    (Lectuer, Essex Business School, University of Essex (E-mail:dvinog@essex.ac.uk))

This paper develops a framework to estimate the probability of default (PD) implied in listed stock options. The underlying option pricing model measures PD as the intensity of a jump diffusion process, in which the underlying stock price jumps to zero at default. We adopt a two-stage calibration algorithm to obtain the precise estimator of PD. In the calibration procedure, we improve the fitness of the option pricing model via the implementation of the time inhomogeneous term structure model in the option pricing model. Since the term structure model perfectly fits the actual term structure, we resolve the estimation bias caused by the poor fitness of the time homogeneous term structure model. It is demonstrated that the PD estimator from listed stock options can provide meaningful insights on the pricing of credit derivatives like credit default swap.

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File URL: http://www.imes.boj.or.jp/research/papers/english/12-E-14.pdf
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Paper provided by Institute for Monetary and Economic Studies, Bank of Japan in its series IMES Discussion Paper Series with number 12-E-14.

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Date of creation: Oct 2012
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Handle: RePEc:ime:imedps:12-e-14
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  1. Bjerksund, Petter & Stensland, Gunnar, 1993. "Closed-form approximation of American options," Scandinavian Journal of Management, Elsevier, vol. 9(Supplemen), pages S87-S99.
  2. 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.
  3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  5. Kristensen, Dennis & Mele, Antonio, 2011. "Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models," Journal of Financial Economics, Elsevier, vol. 102(2), pages 390-415.
  6. Tabak, Benjamin M. & Luduvice, André Victor D. & Cajueiro, Daniel O., 2011. "Modeling default probabilities: The case of Brazil," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 21(4), pages 513-534, October.
  7. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  8. Qi, Min & Zhao, Xinlei, 2011. "Comparison of modeling methods for Loss Given Default," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2842-2855, November.
  9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
  10. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  11. Kyriacos Kyriacou & Jakob B. Madsen & Bryan Mase, 2006. "Does inflation exaggerate the equity premium?," Journal of Economic Studies, Emerald Group Publishing, vol. 33(5), pages 344-356, November.
  12. Vadim Linetsky, 2006. "Pricing Equity Derivatives Subject To Bankruptcy," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 255-282.
  13. Das, Sanjiv R. & Hanouna, Paul, 2009. "Implied recovery," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1837-1857, November.
  14. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  15. Edward I. Altman & Brooks Brady & Andrea Resti & Andrea Sironi, 2005. "The Link between Default and Recovery Rates: Theory, Empirical Evidence, and Implications," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2203-2228, November.
  16. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
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