Idiosyncratic Risk, Systematic Risk and Stochastic Volatility: An Implementation of Merton's Credit Risk Valuation
AbstractWe 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.
Download InfoTo our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 123.
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
credit risk; credit spread; idiosyncratic risk; stochastic voltility; systematic risk;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Pamela Nickell & William Perraudin & Simone Varotto, 2001.
"Stability of ratings transitions,"
Bank of England working papers
133, Bank of England.
- Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
- John Y. Campbell & Martin Lettau & Burton G. Malkiel & Yexiao Xu, 2000.
"Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk,"
NBER Working Papers
7590, National Bureau of Economic Research, Inc.
- John Y. Campbell, 2001. "Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk," Journal of Finance, American Finance Association, vol. 56(1), pages 1-43, 02.
- Malkiel, Burton & Campbell, John & Lettau, Martin & Xu, Yexiao, 2001. "Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk," Scholarly Articles 3128707, Harvard University Department of Economics.
- William N. Goetzmann & Alok Kumar, 2004.
"Equity Portfolio Diversification,"
Yale School of Management Working Papers
ysm17, Yale School of Management.
- N. Hofmann & E. Platen & M. Schweizer, 1992.
"Option Pricing under Incompleteness and Stochastic Volatility,"
Discussion Paper Serie B
209, University of Bonn, Germany.
- Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
- Jan Ericsson & Olivier Renault, 2006.
"Liquidity and Credit Risk,"
Journal of Finance,
American Finance Association, vol. 61(5), pages 2219-2250, October.
- Bekaert, Geert & Wu, Guojun, 2000.
"Asymmetric Volatility and Risk in Equity Markets,"
Review of Financial Studies,
Society for Financial Studies, vol. 13(1), pages 1-42.
- Campbell, John & Taksler, Glen, 2003.
"Equity Volatility and Corporate Bond Yields,"
3153307, Harvard University Department of Economics.
- John Y. Campbell & Glen B. Taksler, 2002. "Equity Volatility and Corporate Bond Yields," Harvard Institute of Economic Research Working Papers 1945, Harvard - Institute of Economic Research.
- John Y. Campbell & Glen B. Taksler, 2002. "Equity Volatility and Corporate Bond Yields," NBER Working Papers 8961, National Bureau of Economic Research, Inc.
- Lucas, Andr‚ & Klaassen, Pieter & Spreij, Peter, 1999.
"An analytic approach to credit risk of large corporate bond and loan portfolios,"
Serie Research Memoranda
0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
- Lucas, Andre & Klaassen, Pieter & Spreij, Peter & Straetmans, Stefan, 2001. "An analytic approach to credit risk of large corporate bond and loan portfolios," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1635-1664, September.
- 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.
- Edwin J. Elton, 2001. "Explaining the Rate Spread on Corporate Bonds," Journal of Finance, American Finance Association, vol. 56(1), pages 247-277, 02.
- Hayette Gatfaoui, 2003. "Risk Disaggregation And Credit Risk Valuation In The Merton Like Way," Finance 0308007, EconWPA.
- Amit Goyal & Pedro Santa-Clara, 2003. "Idiosyncratic Risk Matters!," Journal of Finance, American Finance Association, vol. 58(3), pages 975-1008, 06.
- Bangia, Anil & Diebold, Francis X. & Kronimus, Andre & Schagen, Christian & Schuermann, Til, 2002.
"Ratings migration and the business cycle, with application to credit portfolio stress testing,"
Journal of Banking & Finance,
Elsevier, vol. 26(2-3), pages 445-474, March.
- Anil Bangia & Francis X. Diebold & Til Schuermann, 2000. "Ratings Migration and the Business Cycle, With Application to Credit Portfolio Stress Testing," Center for Financial Institutions Working Papers 00-26, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Merton, Robert C., 1973.
"On the pricing of corporate debt: the risk structure of interest rates,"
684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-70, May.
- Leland, Hayne E & Toft, Klaus Bjerre, 1996.
" Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads,"
Journal of Finance,
American Finance Association, vol. 51(3), pages 987-1019, July.
- Hayne E. Leland and Klaus Bjerre Toft., 1995. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Research Program in Finance Working Papers RPF-259, University of California at Berkeley.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Siem Jan Koopman & Andr� Lucas, 2003.
"Business and Default Cycles for Credit Risk,"
Tinbergen Institute Discussion Papers
03-062/2, Tinbergen Institute, revised 09 Jan 2003.
- Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 97-116.
- Stephen Satchell & Soosung Hwang, 1999.
"Market Risk and the Concept of Fundamental Volatility: Measuring Volatility Across Asset and Derivative Markets and Testing for the Impact of Derivatives Markets on Financial Markets,"
wp99-16, Warwick Business School, Finance Group.
- Hwang, Soosung & Satchell, Stephen E., 2000. "Market risk and the concept of fundamental volatility: Measuring volatility across asset and derivative markets and testing for the impact of derivatives markets on financial markets," Journal of Banking & Finance, Elsevier, vol. 24(5), pages 759-785, May.
- Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 76-84, June.
- Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Duncan Ford).
If references are entirely missing, you can add them using this form.