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The dependence of assets and default threshold with thinning-dependence structure
1. | Department of Mathematics and Center for Financial Engineering, Soochow University, Suzhou 215006, China, China |
References:
[1] |
T. Bielecki and M. Rutkowski, "Credit Risk: Modeling, Valuation and Hedging," Springer Finance, Springer-Verlag, Berlin, 2002. |
[2] |
F. Black and J. Cox, Valuing corporate securities liabilities: Some effects of bond indenture provisions, J. Finan., 31 (1976), 351-367.
doi: 10.2307/2326607. |
[3] |
F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ., 81 (1973), 637-654.
doi: 10.1086/260062. |
[4] |
N. Cai, On first passage times of a hyper-exponential jump diffusion process, Oper. Res. Lett., 37 (2009), 127-134.
doi: 10.1016/j.orl.2009.01.002. |
[5] |
N. Chen and S. G. Kou, Credit spreads, optiomal capital structure, and implied volatility with endogenous defaults and jump risk, Math. Financ., 19 (2009), 343-378.
doi: 10.1111/j.1467-9965.2009.00375.x. |
[6] |
Y. C. Chi, Analysis of expected discounted penalty function for a general jump-diffusion risk model and applications in finance, Insurance Math. Econom., 46 (2010), 385-396.
doi: 10.1016/j.insmatheco.2009.12.004. |
[7] |
P. Collin-Dufresne and R. S. Goldstein, Do credit spreads reflect stationary leverage ratios?, J. Finan., 56 (2001), 1929-1957.
doi: 10.1111/0022-1082.00395. |
[8] |
D. Duffie and K. Singleton, Modeling term structure of defaultable bond, Rev. Financ. Stud., 12 (1999), 687-720.
doi: 10.1093/rfs/12.4.687. |
[9] |
D. Duffie and D. Lando, Term structures of credit spreads with incomplete accounting information, Econometrica, 69 (2001), 633-664.
doi: 10.1111/1468-0262.00208. |
[10] |
F. Dufresne and H. U. Gerber, Risk theory for the compound Poisson process that is perturbed by diffusion, Insurance Math. Econom., 10 (1991), 51-59.
doi: 10.1016/0167-6687(91)90023-Q. |
[11] |
H. U. Gerber and B. Landry, On the discounted penalty at ruin in a jump-diffusion and the perpetual put option, Insurance Math. Econom., 22 (1998), 263-276.
doi: 10.1016/S0167-6687(98)00014-6. |
[12] |
H. U. Gerber and E. S. W. Shiu, On the time value of ruin, N. Amer. Actuarial J., 2 (1998), 48-78. |
[13] |
K. Giesecke and L. Goldberg, Forecasting default in the face of uncertainty, J. Derivatives, 12 (2004), 14-25.
doi: 10.3905/jod.2004.434534. |
[14] |
R. Goldstein, N. Ju and H. Leland, An EBIT-based model of dynamic capital structure, J. Bus., 74 (2001), 483-512.
doi: 10.1086/322893. |
[15] |
B. Hilberink and L. C. G. Rogers, Optimal capital structure and endogenous default, Financ. Stoch, 6 (2002), 237-263.
doi: 10.1007/s007800100058. |
[16] |
J. Z. Huang and M. Huang, How much of the corporate-treasury yield spread is due to credit risk?: A new calibration approach, in "14th Annual Conference on Financial Economics and Accounting," 2003. Available from: http://ssrn.com/abstract=307360. |
[17] |
J. Z. Huang and H. Zhou, Specification analysis of structual credit risk models, in "Finance and Economics Discussion Series," Penn State and Federal Reserve Board, 2008. Available from: http://ssrn.com/paper=1105640. |
[18] |
R. Jarrow and S. Turnbull, Pricing derivatives on financial securities subject to default risk, J. Finan., 50 (1995), 53-86.
doi: 10.2307/2329239. |
[19] |
N. Ju and H. Ou-Yang, Capital structure, debt maturity, and stochastic interest rates, J. Bus., 79 (2006), 2469-2502.
doi: 10.1086/505241. |
[20] |
S. G. Kou, A jump-diffusion model for option pricing, Manag. Sci., 48 (2002), 1086-1101.
doi: 10.1287/mnsc.48.8.1086.166. |
[21] |
S. G. Kou and H. Wang, Option pricing under a double exponential jump diffusion model, Manag. Sci., 50 (2004), 1178-1192. |
[22] |
S. G. Kou and H. Wang, First passage times of a jump diffusion process, Adv. App. Probab., 35 (2003), 504-531. |
[23] |
D. Lando, "Credit Risk Modeling: Theory and Applications," Princeton Series in Finance, Princeton University Press, Princeton, 2004. |
[24] |
H. E. Leland, Corporate debt value, bond covenants, and optimal capital structure, J. Finan., 49 (1994), 1213-1252.
doi: 10.2307/2329184. |
[25] |
H. Leland and K. B. Toft, Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads, J. Finan., 51 (1996), 987-1019.
doi: 10.2307/2329229. |
[26] |
F. Longstaff and E. Schwartz, Valuing risky debt: A new approach, J. Finan., 50 (1995), 789-821.
doi: 10.2307/2329288. |
[27] |
D. B. Madan and H. Unal, Pricing the risks of default, Rev. Deriv. Res., 2 (1998), 121-160.
doi: 10.1007/BF01531333. |
[28] |
R. C. Merton, On the pricing of corporate debt: The risky structure of interest rates, J. Finan., 29 (1974), 449-470.
doi: 10.2307/2978814. |
[29] |
C. A. Ramezani and Y. Zeng, Maximum likelihood estimation of the double exponential jump-diffusion process, Ann. Finan., 3 (2007), 487-507.
doi: 10.1007/s10436-006-0062-y. |
[30] |
S. M. Ross, "Stochastic Processes," Second edition, Wiley Series in Probability and Statistics: Probability and Statistics, John Wiley & Sons, Inc., New York, 1996. |
[31] |
J. Ruf, "Structural Default Models with Jumps," Ph.D thesis, University of Ulm, 2006. |
[32] |
T. Schmidt and A. Novikov, A structural model with unobserved default boundary, Appl. Math. Finan., 15 (2008), 183-203.
doi: 10.1080/13504860701718281. |
[33] |
G. J. Wang and K. C. Yuen, On a correlated aggregate claims model with thinning-dependence structure, Insurance Math. Econom., 36 (2005), 456-468.
doi: 10.1016/j.insmatheco.2005.04.004. |
[34] |
Z. M. Zhang, H. Yang and S. M. Li, The perturbed compound Poisson risk model with two-sided jumps, J. Comput. Appl. Math., 233 (2010), 1773-1784.
doi: 10.1016/j.cam.2009.09.014. |
[35] |
C. S. Zhou, The term structure of credit spreads with jump risk, J. Bank. Finan., 25 (2001), 2015-2040.
doi: 10.1016/S0378-4266(00)00168-0. |
show all references
References:
[1] |
T. Bielecki and M. Rutkowski, "Credit Risk: Modeling, Valuation and Hedging," Springer Finance, Springer-Verlag, Berlin, 2002. |
[2] |
F. Black and J. Cox, Valuing corporate securities liabilities: Some effects of bond indenture provisions, J. Finan., 31 (1976), 351-367.
doi: 10.2307/2326607. |
[3] |
F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ., 81 (1973), 637-654.
doi: 10.1086/260062. |
[4] |
N. Cai, On first passage times of a hyper-exponential jump diffusion process, Oper. Res. Lett., 37 (2009), 127-134.
doi: 10.1016/j.orl.2009.01.002. |
[5] |
N. Chen and S. G. Kou, Credit spreads, optiomal capital structure, and implied volatility with endogenous defaults and jump risk, Math. Financ., 19 (2009), 343-378.
doi: 10.1111/j.1467-9965.2009.00375.x. |
[6] |
Y. C. Chi, Analysis of expected discounted penalty function for a general jump-diffusion risk model and applications in finance, Insurance Math. Econom., 46 (2010), 385-396.
doi: 10.1016/j.insmatheco.2009.12.004. |
[7] |
P. Collin-Dufresne and R. S. Goldstein, Do credit spreads reflect stationary leverage ratios?, J. Finan., 56 (2001), 1929-1957.
doi: 10.1111/0022-1082.00395. |
[8] |
D. Duffie and K. Singleton, Modeling term structure of defaultable bond, Rev. Financ. Stud., 12 (1999), 687-720.
doi: 10.1093/rfs/12.4.687. |
[9] |
D. Duffie and D. Lando, Term structures of credit spreads with incomplete accounting information, Econometrica, 69 (2001), 633-664.
doi: 10.1111/1468-0262.00208. |
[10] |
F. Dufresne and H. U. Gerber, Risk theory for the compound Poisson process that is perturbed by diffusion, Insurance Math. Econom., 10 (1991), 51-59.
doi: 10.1016/0167-6687(91)90023-Q. |
[11] |
H. U. Gerber and B. Landry, On the discounted penalty at ruin in a jump-diffusion and the perpetual put option, Insurance Math. Econom., 22 (1998), 263-276.
doi: 10.1016/S0167-6687(98)00014-6. |
[12] |
H. U. Gerber and E. S. W. Shiu, On the time value of ruin, N. Amer. Actuarial J., 2 (1998), 48-78. |
[13] |
K. Giesecke and L. Goldberg, Forecasting default in the face of uncertainty, J. Derivatives, 12 (2004), 14-25.
doi: 10.3905/jod.2004.434534. |
[14] |
R. Goldstein, N. Ju and H. Leland, An EBIT-based model of dynamic capital structure, J. Bus., 74 (2001), 483-512.
doi: 10.1086/322893. |
[15] |
B. Hilberink and L. C. G. Rogers, Optimal capital structure and endogenous default, Financ. Stoch, 6 (2002), 237-263.
doi: 10.1007/s007800100058. |
[16] |
J. Z. Huang and M. Huang, How much of the corporate-treasury yield spread is due to credit risk?: A new calibration approach, in "14th Annual Conference on Financial Economics and Accounting," 2003. Available from: http://ssrn.com/abstract=307360. |
[17] |
J. Z. Huang and H. Zhou, Specification analysis of structual credit risk models, in "Finance and Economics Discussion Series," Penn State and Federal Reserve Board, 2008. Available from: http://ssrn.com/paper=1105640. |
[18] |
R. Jarrow and S. Turnbull, Pricing derivatives on financial securities subject to default risk, J. Finan., 50 (1995), 53-86.
doi: 10.2307/2329239. |
[19] |
N. Ju and H. Ou-Yang, Capital structure, debt maturity, and stochastic interest rates, J. Bus., 79 (2006), 2469-2502.
doi: 10.1086/505241. |
[20] |
S. G. Kou, A jump-diffusion model for option pricing, Manag. Sci., 48 (2002), 1086-1101.
doi: 10.1287/mnsc.48.8.1086.166. |
[21] |
S. G. Kou and H. Wang, Option pricing under a double exponential jump diffusion model, Manag. Sci., 50 (2004), 1178-1192. |
[22] |
S. G. Kou and H. Wang, First passage times of a jump diffusion process, Adv. App. Probab., 35 (2003), 504-531. |
[23] |
D. Lando, "Credit Risk Modeling: Theory and Applications," Princeton Series in Finance, Princeton University Press, Princeton, 2004. |
[24] |
H. E. Leland, Corporate debt value, bond covenants, and optimal capital structure, J. Finan., 49 (1994), 1213-1252.
doi: 10.2307/2329184. |
[25] |
H. Leland and K. B. Toft, Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads, J. Finan., 51 (1996), 987-1019.
doi: 10.2307/2329229. |
[26] |
F. Longstaff and E. Schwartz, Valuing risky debt: A new approach, J. Finan., 50 (1995), 789-821.
doi: 10.2307/2329288. |
[27] |
D. B. Madan and H. Unal, Pricing the risks of default, Rev. Deriv. Res., 2 (1998), 121-160.
doi: 10.1007/BF01531333. |
[28] |
R. C. Merton, On the pricing of corporate debt: The risky structure of interest rates, J. Finan., 29 (1974), 449-470.
doi: 10.2307/2978814. |
[29] |
C. A. Ramezani and Y. Zeng, Maximum likelihood estimation of the double exponential jump-diffusion process, Ann. Finan., 3 (2007), 487-507.
doi: 10.1007/s10436-006-0062-y. |
[30] |
S. M. Ross, "Stochastic Processes," Second edition, Wiley Series in Probability and Statistics: Probability and Statistics, John Wiley & Sons, Inc., New York, 1996. |
[31] |
J. Ruf, "Structural Default Models with Jumps," Ph.D thesis, University of Ulm, 2006. |
[32] |
T. Schmidt and A. Novikov, A structural model with unobserved default boundary, Appl. Math. Finan., 15 (2008), 183-203.
doi: 10.1080/13504860701718281. |
[33] |
G. J. Wang and K. C. Yuen, On a correlated aggregate claims model with thinning-dependence structure, Insurance Math. Econom., 36 (2005), 456-468.
doi: 10.1016/j.insmatheco.2005.04.004. |
[34] |
Z. M. Zhang, H. Yang and S. M. Li, The perturbed compound Poisson risk model with two-sided jumps, J. Comput. Appl. Math., 233 (2010), 1773-1784.
doi: 10.1016/j.cam.2009.09.014. |
[35] |
C. S. Zhou, The term structure of credit spreads with jump risk, J. Bank. Finan., 25 (2001), 2015-2040.
doi: 10.1016/S0378-4266(00)00168-0. |
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