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

Author

Listed:
  • 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))

Abstract

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.

Suggested Citation

  • 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.
  • Handle: RePEc:ime:imedps:12-e-14
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    File URL: http://www.imes.boj.or.jp/research/papers/english/12-E-14.pdf
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    References listed on IDEAS

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    1. Vadim Linetsky, 2006. "Pricing Equity Derivatives Subject To Bankruptcy," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 255-282.
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    3. 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.
    4. 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.
    5. 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.
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    Cited by:

    1. 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.

    More about this item

    Keywords

    probability of default (PD); option pricing under credit risk; perturbation method;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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