Skip to main content
Article thumbnail
Location of Repository

Structural models of credit with default contagion

By H. Haworth


Multi-asset credit derivatives trade in huge volumes, yet no models exist that are capable of properly accounting for the spread behaviour of dependent companies. In this thesis we consider new ways of incorporating a richer and more realistic dependence structure into multi-firm models. We focus on the structural framework in which firm value is modelled as a geometric Brownian motion, with default as the first hitting time of an exponential default threshold. Specification of a dependence structure consisting of a common driving influence and firm-specific inter-company ties allows for both default causality and default asymmetry and we incorporate default contagion in the first passage framework for the first time. Building on the work by Zhou (2001a), we propose an analytical model for corporate bond yields in the presence of default contagion and two-firm credit default swap baskets. We derive closed-form solutions for credit spreads, and results clearly highlight the importance of dependence assumptions. Extending this framework numerically, we calculate CDS spreads for baskets of three firms with a wide variety of credit dependence specifications. We examine the impact of firm value correlation and credit contagion for symmetric and asymmetric baskets, and incorporate contagion that has a declining impact over time

Topics: Game theory, mathematical finance, economics, social and behavioral sciences
Year: 2006
OAI identifier:

Suggested articles


  1. (1998). A framework for valuing corporate securities. doi
  2. (1997). A jump diffusion approach to modeling credit risk and valuing defaultable securities. Finance and Economic Discussion Series, The Federal Reserve Board,
  3. (2001). A jump-diffusion model for pricing corporate debt securities in a complex capital structure. Quantitative Finance,
  4. (1999). A remark on default risk models.
  5. (1995). A simple approach to valuing risky fixed and floating rate debt.
  6. (2004). A simple model of credit contagion. Working Paper, doi
  7. (2006). A structural model with unobserved default boundary. Working Paper,
  8. (1995). A student introduction.
  9. An analysis of default correlations and multiple defaults.
  10. (2001). An empirical examination of the classical theory of corporate security valuation. Working Paper, Barclays Global Investors,
  11. (1977). An equilibrium characterization of the term structure.
  12. (1999). An Introduction to Copulas.
  13. (2006). Applied Mathematical Finance, doi
  14. (2004). Arbitrage theory in continuous time, 2nd Edition.
  15. (2002). Are jumps in corporate bond yields priced? Modeling contagion via the updating of beliefs. Working Paper,
  16. (1999). Bond pricing with default risk. Working Paper,
  17. (2006). Can structural models price default risk? Evidence from bond and credit derivative markets. Working Paper, doi
  18. (2004). Capital structure and asset prices: Some effects of bankruptcy procedures.
  19. (1984). Contingent claims analysis of corporate capital structure: An empirical investigation.
  20. (2004). Copula methods in finance.
  21. (2006). Copulas: Tales and Facts. Forthcoming, Extremes,
  22. (2005). Correlated defaults in intensity-based models. Mathematical Finance, forthcoming,
  23. (2002). Correlation and dependence in risk management: Properties and pitfalls.
  24. (2003). Credit derivatives pricing models.
  25. (2004). Credit networks and agent games. DPhil thesis,
  26. (2002). Credit risk: modeling, valuation and hedging. doi
  27. (2005). Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk. Working Paper,
  28. (2002). CreditgradesTM .
  29. (2006). Default and information.
  30. (2002). Default compensator, incomplete information, and the term structure of credit spreads. Working Paper, Humboldt-Universitat zu
  31. (1997). Default correlation: An analytical result. Finance and Economic Discussion Series, The Federal Reserve Board,
  32. (1993). Default risk and interest rate risk: The term structure of default spreads. Working Paper,
  33. (2002). Defaultable bonds and default correlation. Working paper,
  34. (1998). Derivatives: The theory and practice of financial engineering.
  35. (1987). Determinants of the ratings and yields on corporate bonds: Tests of the contingent claims model.
  36. (2006). Discussion of ‘Copulas: Tales and Facts,’ by Thomas Mikosch. Forthcoming, Extremes,
  37. (1998). Double lookbacks.
  38. (2006). Dynamic modelling of single-name credits and CDO tranches. Nomura Fixed Income Quant Group,
  39. (2006). Effects of economic interactions on credit risk.
  40. (1992). Elliptic Differential Equations, Theory and Numerical Treatment.
  41. (2004). Evaluating the normal distribution.
  42. (2004). Forecasting default in the face of uncertainty.
  43. (1964). Handbook of Mathematical Functions. doi
  44. Infectious defaults.
  45. (1998). Martingale Methods in Financial Modelling.
  46. (2004). Merton’s model, credit risk, and volatility skews.
  47. (2006). Modeling correlated defaults: First passage model under stochastic volatility. Working Paper,
  48. (2004). Modeling credit risk with partial information.
  49. (2001). Modeling the distance-to-default process of a firm. Working Paper,
  50. (2001). Modelling default correlation in bond portfolios. Working Paper,
  51. (1998). Modelling financial derivatives with Mathematica.
  52. (1998). Numerical integration using sparse grids. Numerical Algorithms,
  53. (2000). On default correlation: A copula function approach.
  54. (2004). On multigrid for anisotropic equations and variational inequalities. Computing and Visualization in Science,
  55. (2002). Optimal capital structure and endogenous default.
  56. (1996). Optimal capital structure, endogenous bankruptcy and the term structure of credit spreads.
  57. (1976). Option pricing when underlying stock returns are discontinuous.
  58. (2006). Pricing CDOs with correlated Variance Gamma distributions. Working Paper,
  59. (2006). Pricing defaultable bonds: A middle-way approach between structural and reduced-form models.
  60. (1995). Pricing derivatives on financial securities subject to credit risk.
  61. (2006). Recovery risk in defaultable debt models: Empirical comparisons and implied recovery rates. Working Paper, doi
  62. (1999). Simulating correlated defaults. Working Paper,
  63. (1997). Strategic debt service.
  64. (2004). Structural models of corporate bond pricing: An empirical analysis. doi
  65. (2003). Successive correlated defaults: Pricing trends and simulation.
  66. (1980). Tables of integrals, series, and products.
  67. (2001). Term structures of credit spreads with incomplete accounting information. doi
  68. (2004). The analytic valuation of multi-asset, one-touch barrier options. Working Paper,
  69. (1995). The impact of default risk on the prices of options and other derivative securities.
  70. (1984). The one-dimensional heat equation, Cannon Encyclopedia of Mathematics and its applications Vol 23.
  71. (1973). The pricing of options and corporate liabilities. doi
  72. (2003). The quintessential option pricing formula. Working Paper,
  73. The term structure of credit spreads with jump risk. doi
  74. (1979). The valuation of compound options.
  75. (2005). The valuation of correlation-dependent credit derivatives using a structural model. Working Paper,
  76. (1993). Valuation of corporate fixed-income securities. Financial Management,
  77. (2006). Valuation of default sensitive claims under imperfect information. Working Paper,
  78. (1998). Valuation of defaultable bonds.
  79. (2003). Valuing corporate liabilities when the default threshold is not an absorbing barrier. Working Paper, Universite´ de Rennes,
  80. (1976). Valuing corporate securities: Some effects of bond indenture provisions. doi
  81. (1997). Valuing risky fixed rate debt: An extension. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.