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Default Risk in Stochastic Volatility Models

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Abstract

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.

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  • 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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    File URL: https://www.ethz.ch/content/dam/ethz/special-interest/mtec/cer-eth/cer-eth-dam/documents/working-papers/WP-10-131.pdf
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    References listed on IDEAS

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    1. Pierre Collin‐Dufresne & Robert S. Goldstein, 2001. "Do Credit Spreads Reflect Stationary Leverage Ratios?," Journal of Finance, American Finance Association, vol. 56(5), pages 1929-1957, October.
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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.

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    More about this item

    Keywords

    stochastic volatility; Merton model; default probabilities; rate of mean reversion;
    All these keywords.

    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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