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.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0404004.
Length: 32 pages
Date of creation: 07 Apr 2004
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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)
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- 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.
- William N. Goetzmann & Alok Kumar, 2008.
"Equity Portfolio Diversification,"
Review of Finance,
European Finance Association, vol. 12(3), pages 433-463.
- William N. Goetzmann & Alok Kumar, 2001. "Equity Portfolio Diversification," NBER Working Papers 8686, National Bureau of Economic Research, Inc.
- William N. Goetzmann & Alok Kumar, 2004. "Equity Portfolio Diversification," Yale School of Management Working Papers ysm17, Yale School of Management.
- Alok Kumar & William N. Goetzmann, 2001. "Equity Portfolio Diversification," Yale School of Management Working Papers ysm236, Yale School of Management.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Heiko Ebens, 2000.
"The Distribution of Stock Return Volatility,"
NBER Working Papers
7933, National Bureau of Economic Research, Inc.
- 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.
- John Y. Campbell & Glen B. Taksler, 2003.
"Equity Volatility and Corporate Bond Yields,"
Journal of Finance,
American Finance Association, vol. 58(6), pages 2321-2350, December.
- Campbell, John & Taksler, Glen, 2003. "Equity Volatility and Corporate Bond Yields," Scholarly Articles 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.
- 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.
- Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
- 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.
- Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- 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.
- Lucas, André & 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.
- Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992.
"Option Pricing Under Incompleteness and Stochastic Volatility,"
Wiley Blackwell, vol. 2(3), pages 153-187.
- N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
- Pierre Collin-Dufresne, 2001. "The Determinants of Credit Spread Changes," Journal of Finance, American Finance Association, vol. 56(6), pages 2177-2207, December.
- Amit Goyal & Pedro Santa-Clara, 2003. "Idiosyncratic Risk Matters!," Journal of Finance, American Finance Association, vol. 58(3), pages 975-1008, 06.
- 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.
- Pamela Nickell & William Perraudin & Simone Varotto, 2001.
"Stability of ratings transitions,"
Bank of England working papers
133, Bank of England.
- Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 97-116.
- 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.
- Thomas C. Wilson, 1998. "Portfolio credit risk," Economic Policy Review, Federal Reserve Bank of New York, issue Oct, pages 71-82.
- Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 76-84, June.
- 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.
- Hayette Gatfaoui, 2003. "Risk Disaggregation And Credit Risk Valuation In The Merton Like Way," Finance 0308007, EconWPA.
- 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.
- Edwin J. Elton, 2001. "Explaining the Rate Spread on Corporate Bonds," Journal of Finance, American Finance Association, vol. 56(1), pages 247-277, 02.
- Nicole El Karoui & Monique Jeanblanc-Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126.
- 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.
- 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.
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