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 techniques 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 InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0404004.
Length: 32 pages
Date of creation: 07 Apr 2004
Date of revision:
Note: Type of Document - pdf; pages: 32
Contact details of provider:
Web page: http://22.214.171.124
Credit risk; credit spread; idiosyncratic risk; stochastic volatility; 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:
- NEP-ALL-2004-04-11 (All new papers)
- NEP-CFN-2004-04-11 (Corporate Finance)
- NEP-FIN-2004-04-11 (Finance)
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.:
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Heiko Ebens, 2000.
"The Distribution of Stock Return Volatility,"
Center for Financial Institutions Working Papers
00-27, Wharton School Center for Financial Institutions, University of Pennsylvania.
- 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.
- 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.
- John Y. Campbell & Glen B. Taksler, 2002.
"Equity Volatility and Corporate Bond Yields,"
NBER Working Papers
8961, National Bureau of Economic Research, Inc.
- 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.
- Campbell, John & Taksler, Glen, 2003. "Equity Volatility and Corporate Bond Yields," Scholarly Articles 3153307, Harvard University Department of Economics.
- Geert Bekaert & Guojun Wu, 1997.
"Asymmetric Volatility and Risk in Equity Markets,"
NBER Working Papers
6022, 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.
- 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.
- 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.
- Thomas C. Wilson, 1998. "Portfolio credit risk," Economic Policy Review, Federal Reserve Bank of New York, issue Oct, pages 71-82.
- Alok Kumar & William N. Goetzmann, 2001.
"Equity Portfolio Diversification,"
Yale School of Management Working Papers
ysm236, Yale School of Management.
- 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.
- 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.
- 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.
- 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.
- Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 76-84, June.
- Hayette Gatfaoui, 2003. "Risk Disaggregation And Credit Risk Valuation In The Merton Like Way," Finance 0308007, EconWPA.
- Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
- 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.
- Edwin J. Elton, 2001. "Explaining the Rate Spread on Corporate Bonds," Journal of Finance, American Finance Association, vol. 56(1), pages 247-277, 02.
- 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.
- 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.
- 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.
- Amit Goyal & Pedro Santa-Clara, 2003. "Idiosyncratic Risk Matters!," Journal of Finance, American Finance Association, vol. 58(3), pages 975-1008, 06.
- Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 97-116.
- Pamela Nickell & William Perraudin & Simone Varotto, 2001.
"Stability of ratings transitions,"
Bank of England working papers
133, Bank of England.
- 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, Financial Econometrics Research Centre.
- 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.
- Pierre Collin-Dufresne, 2001. "The Determinants of Credit Spread Changes," Journal of Finance, American Finance Association, vol. 56(6), pages 2177-2207, December.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).
If references are entirely missing, you can add them using this form.