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Default Risk in Stochastic Volatility Models




We consider a stochastic volatility model of the mean-reverting type to describe the evolution of a firm’s values instead of the classical approach by Merton with geometric Brownian motions. We develop an analytical expression for the default probability. Our simulation results indicate that the stochastic volatility model tends to predict higher default probabilities than the corresponding Merton model if a firm’s credit quality is not too low. Otherwise the stochastic volatility model predicts lower probabilities of default. The results may have implications for various financial applications.

Suggested Citation

  • Hans Gersbach & Nicolae Surulescu, 2010. "Default Risk in Stochastic Volatility Models," CER-ETH Economics working paper series 10/131, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  • Handle: RePEc:eth:wpswif:10-131

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    1. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    2. Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 347-362.
    3. Fabrice Collard & Omar Licandro & Luis A. Puch, 2008. "The short-run Dynamics of Optimal Growth Model with Delays," Annals of Economics and Statistics, GENES, issue 90, pages 127-143.
    4. Boucekkine, Raouf & Germain, Marc & Licandro, Omar & Magnus, Alphonse, 1998. "Creative Destruction, Investment Volatility, and the Average Age of Capital," Journal of Economic Growth, Springer, vol. 3(4), pages 361-384, December.
    5. de la Croix, David & Licandro, Omar, 1999. "Life expectancy and endogenous growth," Economics Letters, Elsevier, vol. 65(2), pages 255-263, November.
    6. Boucekkine, Raouf & Germain, Marc & Licandro, Omar & Magnus, Alphonse, 2001. "Numerical solution by iterative methods of a class of vintage capital models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(5), pages 655-669, May.
    7. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute.
    8. Jody Overland & Christopher D. Carroll & David N. Weil, 2000. "Saving and Growth with Habit Formation," American Economic Review, American Economic Association, vol. 90(3), pages 341-355, June.
    9. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
    10. Raouf Boucekkine & David De La Croix & Omar Licandro, 2004. "MODELLING VINTAGE STRUCTURES WITH DDEs: PRINCIPLES AND APPLICATIONS," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 151-179.
    11. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
    12. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    13. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
    14. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 104(2), pages 340-375, June.
    15. Boyer, Marcel, 1978. "A Habit Forming Optimal Growth Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 585-609, October.
    16. Peeters, Marga, 1996. "Investment gestation lags: The difference between time-to-build and delivery lags," MPRA Paper 28549, University Library of Munich, Germany.
    17. Winkler, Ralph & Brandt-Pollmann, Ulrich & Moslener, Ulf & Schlöder, Johannes, 2005. "On the Transition from Instantaneous to Time-Lagged Capital Accumilation: The Case of Leontief Type Production Functions," ZEW Discussion Papers 05-30, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    18. El-Hodiri, Mohamed A & Loehman, Edna & Whinston, Andrew B, 1972. "An Optimal Growth Model with Time Lags," Econometrica, Econometric Society, vol. 40(6), pages 1137-1146, November.
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    Cited by:

    1. Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," Working Papers - Mathematical Economics 2012-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.

    More about this item


    stochastic volatility; Merton model; default probabilities; rate of mean reversion;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill


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