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

  • Hayette Gatfaoui

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.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 123.

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Length: 40
Date of creation: 01 Apr 2004
Date of revision:
Publication status: Forthcoming in Greg N. Gregoriou Eds., Chapter 6, Advances in Risk Management, Palgrave-MacMillan, September 2006
Handle: RePEc:uts:rpaper:123
Contact details of provider: Postal: PO Box 123, Broadway, NSW 2007, Australia
Phone: +61 2 9514 7777
Fax: +61 2 9514 7711
Web page: http://www.qfrc.uts.edu.au/

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  18. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September.
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