IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00589918.html
   My bibliography  Save this paper

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

Author

Listed:
  • Hayette Gatfaoui

    (Pôle Finance Responsable - Rouen Business School - Rouen Business School)

Abstract

We extend the credit risk valuation framework introduced by Gatfaoui 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.

Suggested Citation

  • Hayette Gatfaoui, 2006. "Idiosyncratic Risk, Systematic Risk and Stochastic Volatility: An Implementation of Merton's Credit Risk Valuation," Post-Print hal-00589918, HAL.
    • Handle: RePEc:hal:journl:hal-00589918
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below 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.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 97-116, April.
    2. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    3. John Y. Campbell & Martin Lettau & Burton G. Malkiel & Yexiao Xu, 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, February.
    4. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    5. Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(2), pages 76-84, June.
    6. Delianedis, Gordon & Geske, Robert, 2001. "The Components of Corporate Credit Spreads: Default, Recovery, Tax, Jumps, Liquidity, and Market Factors," University of California at Los Angeles, Anderson Graduate School of Management qt32x284q3, Anderson Graduate School of Management, UCLA.
    7. André Lucas & Siem Jan Koopman, 2005. "Business and default cycles for credit risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(2), pages 311-323.
    8. Nickell, Pamela & Perraudin, William & Varotto, Simone, 2000. "Stability of rating transitions," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 203-227, January.
    9. 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.
    10. William N. Goetzmann & Alok Kumar, 2008. "Equity Portfolio Diversification," Review of Finance, European Finance Association, vol. 12(3), pages 433-463.
    11. 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 449-470, May.
    12. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    13. Jan Ericsson & Olivier Renault, 2006. "Liquidity and Credit Risk," Journal of Finance, American Finance Association, vol. 61(5), pages 2219-2250, October.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. repec:bla:jfinan:v:58:y:2003:i:3:p:975-1008 is not listed on IDEAS
    20. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
    21. 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, April.
    22. 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.
    23. Hayette Gatfaoui, 2003. "Risk Disaggregation And Credit Risk Valuation In The Merton Like Way," Finance 0308007, University Library of Munich, Germany.
    24. Edwin J. Elton & Martin J. Gruber & Deepak Agrawal & Christopher Mann, 2001. "Explaining the Rate Spread on Corporate Bonds," Journal of Finance, American Finance Association, vol. 56(1), pages 247-277, February.
    25. 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.
    26. 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 637-654, May-June.
    27. Giesecke, Kay & Weber, Stefan, 2003. "Cyclical correlations, credit contagion, and portfolio losses," SFB 373 Discussion Papers 2003,11, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    28. Thomas C. Wilson, 1998. "Portfolio credit risk," Economic Policy Review, Federal Reserve Bank of New York, vol. 4(Oct), pages 71-82.
    29. 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.
    30. João L. C. Duque & Patrícia Teixeira Lopes, 2003. "Maturity and volatility effects on UK smiles," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 2(3), pages 173-193, December.
    31. 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.
    32. Pierre Collin-Dufresn & Robert S. Goldstein & J. Spencer Martin, 2001. "The Determinants of Credit Spread Changes," Journal of Finance, American Finance Association, vol. 56(6), pages 2177-2207, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nakashima, Kiyotaka & Saito, Makoto, 2009. "Credit spreads on corporate bonds and the macroeconomy in Japan," Journal of the Japanese and International Economies, Elsevier, vol. 23(3), pages 309-331, September.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. André Lucas & Siem Jan Koopman, 2005. "Business and default cycles for credit risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(2), pages 311-323.
    2. Ramaprasad Bhar, 2010. "Stochastic Filtering with Applications in Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736, August.
    3. Ephraim Clark & Selima Baccar, 2018. "Modelling credit spreads with time volatility, skewness, and kurtosis," Annals of Operations Research, Springer, vol. 262(2), pages 431-461, March.
    4. Astrid Van Landschoot, 2004. "Determinants of Euro Term Structure of Credit Spreads," Working Paper Research 57, National Bank of Belgium.
    5. Maalaoui Chun, Olfa & Dionne, Georges & François, Pascal, 2014. "Credit spread changes within switching regimes," Journal of Banking & Finance, Elsevier, vol. 49(C), pages 41-55.
    6. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    7. Nakashima, Kiyotaka & Saito, Makoto, 2009. "Credit spreads on corporate bonds and the macroeconomy in Japan," Journal of the Japanese and International Economies, Elsevier, vol. 23(3), pages 309-331, September.
    8. Annaert, Jan & De Ceuster, Marc & Van Roy, Patrick & Vespro, Cristina, 2013. "What determines Euro area bank CDS spreads?," Journal of International Money and Finance, Elsevier, vol. 32(C), pages 444-461.
    9. Avino, Davide & Nneji, Ogonna, 2014. "Are CDS spreads predictable? An analysis of linear and non-linear forecasting models," International Review of Financial Analysis, Elsevier, vol. 34(C), pages 262-274.
    10. Landschoot, Astrid Van, 2008. "Determinants of yield spread dynamics: Euro versus US dollar corporate bonds," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2597-2605, December.
    11. van Landschoot, A., 2003. "The Term Structure of Credit Spreads on Euro Corporate Bonds," Other publications TiSEM f5164bb2-6597-48c4-8b44-d, Tilburg University, School of Economics and Management.
    12. Liuren Wu & Frank Xiaoling Zhang, 2008. "A No-Arbitrage Analysis of Macroeconomic Determinants of the Credit Spread Term Structure," Management Science, INFORMS, vol. 54(6), pages 1160-1175, June.
    13. Ericsson, Jan & Reneby, Joel, 2003. "Valuing Corporate Liabilities," SIFR Research Report Series 15, Institute for Financial Research.
    14. Song Han & Xing Zhou, 2014. "Informed Bond Trading, Corporate Yield Spreads, and Corporate Default Prediction," Management Science, INFORMS, vol. 60(3), pages 675-694, March.
    15. van Landschoot, A., 2003. "The Term Structure of Credit Spreads on Euro Corporate Bonds," Discussion Paper 2003-046, Tilburg University, Center for Economic Research.
    16. Han-Hsing Lee, 2020. "Distress risk, product market competition, and corporate bond yield spreads," Review of Quantitative Finance and Accounting, Springer, vol. 55(3), pages 1093-1135, October.
    17. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224.
    18. Jang, Bong-Gyu & Rhee, Yuna & Yoon, Ji Hee, 2016. "Business cycle and credit risk modeling with jump risks," Journal of Empirical Finance, Elsevier, vol. 39(PA), pages 15-36.
    19. Brown, Alessio J. G. & Žarnić, Žiga, 2003. "Explaining the increased German credit spread: The role of supply factors," Kiel Advanced Studies Working Papers 412, Kiel Institute for the World Economy (IfW Kiel).
    20. Van Landschoot, Astrid, 2004. "Determinants of euro term structure of credit spreads," Working Paper Series 397, European Central Bank.

    More about this item

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00589918. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.