Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk

Mathematical Finance

Volumn 19, Issue 3, 2009, Pages 343-378

  Chen, Nan ^a   Kou, S G ^b,c  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b Och Spine at New York Presbyterian Hospitals   (United States)

^c 312 Mudd Building ^*  (United States)

Author keywords

Capital structure; Credit risk; Implied volatility; Jump diffusion; Smooth pasting; Yield spreads

Indexed keywords

EID: 67650784382     PISSN: 09601627     EISSN: 14679965     Source Type: Journal    
DOI: 10.1111/j.1467-9965.2009.00375.x     Document Type: Article

References (92)

1. Abate, J., and W. Whitt (1992 The Fourier-series Method for Inverting Transforms of Probability Distributions, Queueing Syst. 10, 5 88.
2. Anderson, R., and S. Sundaresan (1996 Design and Valuation of Debt Contracts, Rev. Financ. Stud. 9, 37 68.
3. Benaim, S., and P. Friz (2006a Regular Variation and Smile Asymptotics, in Math. Finance, in press.
4. Benaim, S., and P. Friz (2006b Smile Asymptotics, II: Models with Known MGF, Preprint, Cambridge University.
5. Bhattacharya, S. (1998 Corporate Finance and the Legacy of Miller and Modigliani, J. Economic Perspectives 2, 135 147.
6. Bielecki, T. R., and M. Rutkowski (2002 Credit Risk: Modeling, Valuation, and Hedging, Berlin : Springer.
7. Bielecki, T. R., M. Jeanblanc, and M. Rutkowski (2004 Completeness of a General Semimartingale Markets Under Constrained Trading, Working Paper, Illinois Institute of Technology.
8. Bielecki, T. R., M. Jeanblanc, and M. Rutkowski (2005 PDE Approach to Valuation and Hedging of Credit Derivatives, Working Paper, Illinois Institute of Technology.
9. Black, F. (1976 Studies in Stock Price's Volatility Changes in Proceedings of the 1976 Meeting of the American Statistics Association, Business and Economics Sections, 177 181.
10. Black, F., and J. Cox (1976 Valuing Corporate Securities Liabilities: Some Effects of Bond Indenture Provisions, J. Finance 31, 351 367.
11. Black, F., and M. Scholes (1973 The Pricing of Options and Corporate Liabilities, J. Polit. Econ. 81, 637 654.
12. Boyarchenko, S. (2000 Endogenous Default under Lévy Processes, Working Paper, University of Texas, Austin.
13. Brealey, R. A., and S. C. Myers (2001 Principles of Corporate Finance, 6th edition. New York : McGraw-Hill.
14. Bradley, M., G. Jarrell, and E. H. Kim (1984 On the Existence of an Optimal Capital Structure: Theory and Evidence, J. Finance 39, 857 878.
15. Carr, P., and V. Linetsky (2006 A Jump to Default Extended CEV Model: An Application of Bessel Processes, Finance Stochast. 10, 303 330. (Pubitemid 44290757)
16. Çetin, U., R. Jarrow, P. Protter, and Y. Yildirim (2004 Modeling Credit Risk with Partial Information, Ann. Appl. Probab. 14, 1167 1178. (Pubitemid 41449214)
17. Cremers, M., J. Driessen, P. Maenhout, and D. Weinbaum (2005a Individual Stock-option Prices and Credit Spreads, Working Paper, Yale School of Management.
18. Cremers, M., J. Driessen, P. Maenhout, and D. Weinbaum (2005b Explaining the Level of Credit Spreads: Option-implied Jump Risk Premia in a Firm Value Model, Working Paper, Yale School of Management.
19. Collin-Dufresne, P., and R. S. Goldstein (2001 Do Credit Spreads Reflect Stationary Leverage Ratios? J.Finance 56, 1929 1957. (Pubitemid 33581924)
20. Collin-Dufresne, P., R. S. Goldstein, and J. Hugonnier (2001 A General Formula for Valuing Defaultable Securities, Econometrica 72, 1377 1407.
21. Collin-Dufresne, P., R. S. Goldstein, and J. Hugonnier (2003 Is Credit Event Risk Priced? Modeling Contagion via the Updating of Beliefs, Working Paper, Carnegie Mellon University.
22. Cont, R., and P. Tankov (2003 Financial Modelling with Jump Processes, London : Chapman & Hall/CRC Press.
23. Dao, T. B., and M. Jeanblanc (2005 A Double Exponential Structural Jump Diffusion Model with Endogenous Default Barrier, Working Paper, Université d'Evry Val d'Essonne.
24. Das, S. R. (1995 Credit Rsk Derivatives, J. Derivatives 2, 7 23.
25. Duffee, G. R. (1998 The Relation between Treasury Yields and Corporate Bond Yield Spreads, J. Finance 53, 2225 2241. (Pubitemid 128639715)
26. Duffie, D., and D. Lando (2001 Term Structures of Credit Spreads with Incomplete Accounting Information, Econometrica 69, 599 632.
27. Duffie, D., and K. J. Singleton (1999 Modeling Term Structures of Defaultable Bonds, Rev. Financ. Stud. 12, 687 720.
28. Duffie, D., and K. J. Singleton (2003 Credit Risk: Pricing, Measurement, and Management, Princeton, NJ : Princeton University Press.
29. Eom, Y. H., J. Helwege, and J. Z. Huang (2004 Structrual Models of Corporate Bond Pricing: An Empirical Analysis, Rev. Financ. Stud. 17, 499 544. (Pubitemid 39159591)
30. Fons, J. (1994 Using Default Rates to Model the Term Structure of Credit Risk, Financ. Analysts J. 50, 25 32.
31. Fouque, J., R. Sircar, and K. Solna (2004 Stochastic Volatility Effects on Defaultable Bonds, Working Paper, NC State University, Princeton University, and UC Irvine.
32. Friend, I., and L. Lang (1988 An Empirical Test of the Impact of Managerial Self-interest on Corporate Structure, J. Business 43, 271 281.
33. Gibbons, R. S. (1992 Game Theory for Applied Economists, Princeton, NJ : Princeton University Press.
34. Giesecke, K. (2001 Default and Information, Working Paper, Cornell University.
35. Giesecke, K. (2004 Correlated Default with Incomplete Information, J. Banking Finance 28, 1521 1545. (Pubitemid 38670712)
36. Giesecke, K., and L. Goldberg (2003 The Market Price of Credit Risk, Working Paper, Cornell University.
37. Goldstein, R., N. Ju, and H. Leland (2001 An EBIT-based Model of Dynamic Capital Structure, J. Business 74, 483 512. (Pubitemid 33357091)
38. Guo, X., R. A. Jarrow, and Y. Zeng (2005 Information Reduction in Credit Risk Models, Working Paper, Cornell University.
39. Harris, M., and A. Raviv (1991 The Theory of Capital Structure, J. Finance 46, 297 355.
40. He, J., W. Hu, and L. Lang (2000 Credit Spread Curves and Credit Ratings, Working Paper, Chinese University of Hong Kong.
41. Helwege, J., and C. M. Turner (1999 The Slope of the Credit Yield Curve for Speculative-grade Issuers, J. Finance 54, 1869 1884.
42. Hilberink, B., and L. C. G. Rogers (2002 Optimal Capital Structure and Endogenous Default, Finance Stochast. 6, 237 263.
43. Huang J., and M. Huang (2003 How Much of the Corporate-treasury Yield Spread Is due to Credit Risk? Working Paper, Penn. State University and Stanford University.
44. Hull, J., I. Nelken, and A. White (2004 Merton's Model, Credit Risk, and Volatility Skews, J. Credit Risk 1, 1 27.
45. Hurd, T. R., and A. Kuznetsov (2005a Affine Markov Chain Models of Multifirm Credit Migration, Working Paper, McMaster Univ.
46. Hurd, T. R., and A. Kuznetsov (2005b Fast CDO Computations in the Affine Markov Chain Model, Working Paper, McMaster Univ.
47. Jarrow, R. A., and P. Protter (2004 Structural versus Reduced-form Models: A New Information Based Perspective, J. Invest. Manag. 2, 34 43.
48. Jarrow, R. A., and S. Turnbull (1995 Pricing Derivartives on Financial Securities Subject to Credit Risk, J. Finance 50, 53 86.
49. Jarrow, R. A., D. Lando, and S. Turnbull (1997 A Markov Model for the Term Structure of Credit Spreads, Rev. Financ. Stud. 10, 481 523.
50. Jones, E., S. Mason, and E. Rosenfeld (1984 Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation, J. Finance 39, 611 625.
51. Ju, N., and H. Ou-Yang (2006 Capital Structure, Debt Maturity, and Stochastic Interest Rates, J. Business 79, 2469 2502.
52. Kijima, M. (2002 Stochatic Processes with Applications in Finance, Boca Raton, FL : Chapman and Hall.
53. Kijima, M., and T. Suzuki (2001 A Jump-diffusion Model for Pricing Corporate Debt Securities in a Complex Capital Structure, Quant. Finance 1, 611 620.
54. Kim, W. S., and E. H. Sorensen (1986 Evidence on the Impact of the Agency Costs of Debt in Corporate Debt Policy, J. Financ. Quant. Analysis 21, 131 144.
55. Kou, S. G. (2002 A Jump Diffusion Model for Option Pricing, Manag. Sci. 48, 1086 1101.
56. Kou, S. G., and H. Wang (2003 First Passage Times of a Jump Diffusion Process, Adv. Appl. Probab. 35, 504 531.
57. Kou, S. G., G. Petrella, and H. Wang (2005 Pricing Path-dependent Options with Jump Risk via Laplace Transforms, Kyoto Econ. Rev. 74, 1 23.
58. Kyprianou, A., and B. Surya (2007 Principles of Smooth and Continuous Fit in the Determination of Endogenous Bankruptcy Levels, Finance Stochast. 11, 131 152.
59. Lando, D. (2004 Credit Risk Modelling: Theory and Applications, Princeton, NJ : Princeton University Press.
60. Le Courtois, O., and F. Quittard-Pinon (2006 Risk-neutral and Actual Default Probabilities with an Endogenous Bankruptcy Jump-diffusion Model, Asia Pac. Financ. Market. 13, 11 39.
61. Leland, H. E. (1994 Corporate Debt Value, Bond Covenants, and Optimal Capital Sturcture, J. Finance 49, 1213 1252.
62. Leland, H. E. (1995 Bond Prices, Yield Spreads, and Optimal Capital Structure with Default Risk, Working Paper, Finance Dept., UC Berkeley.
63. Leland, H. E. (1998 Agency Costs, Risk Management, and Capital Structure, J. Finance 53 (4 1213 1243. (Pubitemid 128348168)
64. Leland, H. E. (2004 Predictions of Default Probabilities in Structural Models of Debt, J. Invest. Manag. 2 (2 5 20.
65. Leland, H., and K. B. Toft (1996 Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads, J. Finance 51, 987 1019.
66. Linetsky, V. (2006 Pricing Equity Derivatives Subject to Bankruptcy, Math. Finance 16, 255 282.
67. Long, M., and I. Malitz (1985 The Investment-Finance Nexus: Some Empirical Evidence, Midland Corporate Finance J. 3, 53 59.
68. Longstaff, F., and E. Schwartz (1995 Valuing Risky Debt: A New Approach, J. Finance 50, 789 821.
69. Lucas, R. E. (1978 Asset Prices in an Exchange Economy, Econometrica 46, 1429 1445.
70. Madan, D. B., and H. Unal (1998 Pricing the Risks of Default, Rev. Derivatives Res. 2, 121 160.
71. Masulis, R. W. (1988 The Debt/Equity Choice, New York : Ballinger Publishing Company.
72. Medova, E. A., and R. G. Smith (2004 Pricing Equity Default Swaps Using Structural Credit Models, Working Paper, Judge Institute of Management, Univ. of Cambridge.
73. Mella-Barral, P., and W. Perraudin (1997 Strategic Debt Service, J. Finance V, 531 556.
74. Merton, R. C. (1974 On the Pricing of Corporate Debt: The Risky Structure of Interest Rates, J. Finance V, 449 470.
75. Merton, R. C. (1976 Option Pricing When Underlying Stock Returns Are Discontinuous, J. Financ. Econ. 3, 125 144.
76. Metayer, B. (2003 A Double Exponential Jump Diffusion Process to Modelling Risky Bond Prices, Working Paper, Swiss Banking Institute, University of Zurich.
77. Miller, M. H. (1998 The Modigliani-Miller Propositions after Thirty Years, J. Econ. Perspect. 2, 99 120.
78. Modigliani, F. (1998 MM-Past, Present, Future, J. Econ. Perspect. 2, 149 158.
79. Modigliani, F., and M. Miller (1958 The Cost of Capital, Corporation Finance and the Theory of Investment, American Economic Review 48, 261 297.
80. Naik, V., and M. Lee (1990 General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns, Rev. Financ. Stud. 3, 493 521.
81. Ravid, S. A. (1988 On Iterations of Production and Financial Decisions, Financ. Manag. 8, 87 99.
82. Renault, E., and N. Touzi (1996 Option Hedging and Implied Volatilities in a Stochastic Volatility Model, Math. Finance 6, 279 302.
83. Ross, S. A. (1988 Comments on the Modigliani-Miller Propositions, J. Econ. Perspect. 2, 127 133.
84. Sarig, O., and A. Warga (1989 Some Empirical Estimates of the Risk Structure of Interest Rates, J. Finance 44, 1351 1360.
85. Schmid, B. (2004 Credit Risk Pricing Models: Theory and Practice, New York : Springer.
86. Schönbucher, P. (2003 Credit Derivatives Pricing Models: Models, Pricing and Implementation, Chichester, UK : Wiley.
87. Sirbu, M., and S. Shreve (2005 A Two-person Game for Pricing Convertible Bonds, Working Paper, Carnegie Mellon Univ.
88. Sircar, K. R., and G. Papanicolaou (1999 Stochastic Volatility, Smile & Asymptotics, Appl. Math. Finance 6, 107 145.
89. Stiglitz, J. E. (1998 Why Financial Structure Matters, J. Econ. Perspect. 2, 121 126.
90. Titman, S., and R. Wessels (1988 The Determinants of Capital Stucture Choice, J. Finance 43, 1 10.
91. Toft, K. B., and B. Prucyk (1997 Options on Leveraged Equity: Theory and Empirical Tests, J. Finance 52, 1151 1180.
92. Zhou, C. (2001 The Term Structure of Credit Spreads with Jump Risk, J. Banking Finance 25, 2015 2040. (Pubitemid 33623512)