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Idiosyncratic Risk, Systematic Risk and Stochastic Volatility: An Implementation of Merton's Credit Risk Valuation

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  • Hayette Gatfaoui

Abstract

We extend the credit risk valuation framework introduced by Gatfaoui (2003) to stochastic volatility models. We state a general setting for valuing risky debt in the light of systematic risk and idiosyncratic risk, which are known to affect each risky asset in the financial market. The option nature of corporate debt allows then to account for the well-known volatility smile along with two documented determinants, namely stochastic volatility and market risk. Under some regularity conditions, we specify diffusion functionals leading to an asymptotically (relative to time) mean reverting volatility process. The behavior of such a specification is studied along with simulation tehniques since debt is valued via a call on the firm assets value. Specifically, our examination resorts to Monte Carlo accelerators to realize related simulations. First, we consider the evolution of stochastic volatility for given parameter values. Then, we assess its impact on both risky debt and the related credit spread.

Suggested Citation

  • Hayette Gatfaoui, 2004. "Idiosyncratic Risk, Systematic Risk and Stochastic Volatility: An Implementation of Merton's Credit Risk Valuation," Research Paper Series 123, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:123
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    Cited by:

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    2. Carbajal-De-Nova, Carolina & Venegas-Martínez, Francisco, 2019. "On the paradigm shift of asset pricing models, before and after the global financial crisis: a literature review," Panorama Económico, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 15(29), pages 7-38, Primer se.
    3. Issouf Soumaré & Ernest Tafolong, 2017. "Risk-based capital for credit insurers with business cycles and dynamic leverage," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 597-612, April.

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    More about this item

    Keywords

    credit risk; credit spread; idiosyncratic risk; stochastic voltility; systematic risk;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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