The pricing of credit risky securities under stochastic interest rate model with default correlation

Anjiao Wang; Zhong Xing Ye

Applications of Mathematics (2013)

  • Volume: 58, Issue: 6, page 703-727
  • ISSN: 0862-7940

Abstract

top
In this paper, we study the pricing of credit risky securities under a three-firms contagion model. The interacting default intensities not only depend on the defaults of other firms in the system, but also depend on the default-free interest rate which follows jump diffusion stochastic differential equation, which extends the previous three-firms models (see R. A. Jarrow and F. Yu (2001), S. Y. Leung and Y. K. Kwok (2005), A. Wang and Z. Ye (2011)). By using the method of change of measure and the technology (H. S. Park (2008), R. Hao and Z. Ye (2011)) of dealing with jump diffusion processes, we obtain the analytic pricing formulas of defaultable zero-coupon bonds. Moreover, by the ``total hazard construction'', we give the analytic pricing formulas of credit default swap (CDS).

How to cite

top

Wang, Anjiao, and Ye, Zhong Xing. "The pricing of credit risky securities under stochastic interest rate model with default correlation." Applications of Mathematics 58.6 (2013): 703-727. <http://eudml.org/doc/260601>.

@article{Wang2013,
abstract = {In this paper, we study the pricing of credit risky securities under a three-firms contagion model. The interacting default intensities not only depend on the defaults of other firms in the system, but also depend on the default-free interest rate which follows jump diffusion stochastic differential equation, which extends the previous three-firms models (see R. A. Jarrow and F. Yu (2001), S. Y. Leung and Y. K. Kwok (2005), A. Wang and Z. Ye (2011)). By using the method of change of measure and the technology (H. S. Park (2008), R. Hao and Z. Ye (2011)) of dealing with jump diffusion processes, we obtain the analytic pricing formulas of defaultable zero-coupon bonds. Moreover, by the ``total hazard construction'', we give the analytic pricing formulas of credit default swap (CDS).},
author = {Wang, Anjiao, Ye, Zhong Xing},
journal = {Applications of Mathematics},
keywords = {credit risk; default correlation; defaultable bond; credit default swap; default intensity; credit risk pricing; credit default swaps; correlated default rates},
language = {eng},
number = {6},
pages = {703-727},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The pricing of credit risky securities under stochastic interest rate model with default correlation},
url = {http://eudml.org/doc/260601},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Wang, Anjiao
AU - Ye, Zhong Xing
TI - The pricing of credit risky securities under stochastic interest rate model with default correlation
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 6
SP - 703
EP - 727
AB - In this paper, we study the pricing of credit risky securities under a three-firms contagion model. The interacting default intensities not only depend on the defaults of other firms in the system, but also depend on the default-free interest rate which follows jump diffusion stochastic differential equation, which extends the previous three-firms models (see R. A. Jarrow and F. Yu (2001), S. Y. Leung and Y. K. Kwok (2005), A. Wang and Z. Ye (2011)). By using the method of change of measure and the technology (H. S. Park (2008), R. Hao and Z. Ye (2011)) of dealing with jump diffusion processes, we obtain the analytic pricing formulas of defaultable zero-coupon bonds. Moreover, by the ``total hazard construction'', we give the analytic pricing formulas of credit default swap (CDS).
LA - eng
KW - credit risk; default correlation; defaultable bond; credit default swap; default intensity; credit risk pricing; credit default swaps; correlated default rates
UR - http://eudml.org/doc/260601
ER -

References

top
  1. Artzner, P., Delbaen, F., 10.1111/j.1467-9965.1995.tb00064.x, Math. Finance 5 (1995), 187-195. (1995) Zbl0866.90047DOI10.1111/j.1467-9965.1995.tb00064.x
  2. Bai, Y.-F., Hu, X.-H., Ye, Z.-X., 10.1007/s10483-007-1211-9, Appl. Math. Mech., Engl. Ed. 28 (2007), 1643-1649. (2007) Zbl1231.62186MR2440462DOI10.1007/s10483-007-1211-9
  3. Chen, L., Filipovic, D., Pricing credit default swaps under default correlations and counterparty risk, Working paper of Princeton University Princeton (2003). (2003) 
  4. Collin-Dufresne, P., Goldstein, R., Hugonnier, J., 10.1111/j.1468-0262.2004.00538.x, Econometrica 72 (2004), 1377-1407. (2004) Zbl1141.91431MR2077487DOI10.1111/j.1468-0262.2004.00538.x
  5. Collin-Dufresne, P., Solnik, B., 10.1111/0022-1082.00357, The Journal of Finance 56 (2001), 1095-1115. (2001) DOI10.1111/0022-1082.00357
  6. Duffee, G. R., 10.1093/rfs/12.1.197, Review of Financial Studies 12 (1999), 197-226. (1999) DOI10.1093/rfs/12.1.197
  7. Duffie, D., Lando, D., 10.1111/1468-0262.00208, Econometrica 69 (2001), 633-664. (2001) Zbl1019.91022MR1828538DOI10.1111/1468-0262.00208
  8. Duffie, D., Schroder, M., Skiadas, C., 10.1214/aoap/1035463324, Ann. Appl. Probab. 6 (1996), 1075-1090. (1996) Zbl0868.90008MR1422978DOI10.1214/aoap/1035463324
  9. Duffie, D., Singleton, K. J., 10.1093/rfs/12.4.687, Review of Financial Studies 12 (1999), 687-720. (1999) DOI10.1093/rfs/12.4.687
  10. Hao, R., Ye, Z., The intensity model for pricing credit securities with jump diffusion and counterparty risk, Math. Probl. Eng. 2011 Article ID 412565 (2011). (2011) Zbl1213.91171MR2794329
  11. Harrison, J. M., Kreps, D. M., 10.1016/0022-0531(79)90043-7, J. Econ. Theory 20 (1979), 381-408. (1979) Zbl0431.90019MR0540823DOI10.1016/0022-0531(79)90043-7
  12. Harrison, J. M., Pliska, S. R., 10.1016/0304-4149(81)90026-0, Stochastic Processes Appl. 11 (1981), 215-260. (1981) Zbl0482.60097MR0622165DOI10.1016/0304-4149(81)90026-0
  13. Hull, J., White, A., 10.3905/jod.2001.319153, Journal of Derivatives 8 (2001), 12-22. (2001) DOI10.3905/jod.2001.319153
  14. Jarrow, R. A., Lando, D., Turnbull, S. M., 10.1093/rfs/10.2.481, Review of Financial Studies 10 (1997), 481-523. (1997) DOI10.1093/rfs/10.2.481
  15. Jarrow, R. A., Turnbull, S. M., 10.1111/j.1540-6261.1995.tb05167.x, Journal of Finance 50 (1995), 53-86. (1995) DOI10.1111/j.1540-6261.1995.tb05167.x
  16. Jarrow, R. A., Yildirim, Y., 10.3905/jfi.2002.319308, Journal of Fixed Income 11 (2002), 7-19. (2002) DOI10.3905/jfi.2002.319308
  17. Jarrow, R. A., Yu, F., 10.1111/0022-1082.00389, Journal of Finance 56 (2001), 1765-1799. (2001) DOI10.1111/0022-1082.00389
  18. Kim, M. A., Kim, T. S., 10.21314/JOR.2004.104, Journal of Risk 6 (2003), 49-80. (2003) DOI10.21314/JOR.2004.104
  19. Lando, D., 10.1007/BF01531332, Review of Derivatives Research 2 (1998), 99-120. (1998) DOI10.1007/BF01531332
  20. Leung, S. Y., Kwok, Y. K., Credit default swap valuation with counterparty risk, The Kyoto Economic Review 74 (2005), 25-45. (2005) 
  21. Litterman, R. B., Iben, T., 10.3905/jpm.1991.409331, The Journal of Portfolio Management 17 (1991), 52-64. (1991) DOI10.3905/jpm.1991.409331
  22. Madan, D. B., Unal, H., 10.1007/BF01531333, Review of Derivatives Research 2 (1998), 121-160. (1998) DOI10.1007/BF01531333
  23. Park, H. S., 10.1016/j.jkss.2008.06.001, J. Korean Statist. Soc. 37 (2008), 355-363. (2008) Zbl1293.60082MR2467902DOI10.1016/j.jkss.2008.06.001
  24. Shreve, S. E., Stochastic Calculus for Finance II: continuous-time model, Springer New York (2007). (2007) MR2057928
  25. Wang, A., Ye, Z., Credit risky securities valuation under a contagion model with interacting intensities, J. Appl. Math. 2011 (2011), Article ID 158020. (2011) Zbl1223.91039MR2824918
  26. Wang, A. J., Ye, Z. X., The valuation of credit default swap under a three-firms hyperbolic attenuation contagion model, J. Shanghai Jiaotong Univ. 12 (2011), 48-52. (2011) MR2964150
  27. Yu, F., Correlated defaults and the valuation of defaultable securities, Working paper of University of California Irvine (2004). (2004) 
  28. Zheng, H., Jiang, L., 10.1007/s00780-009-0091-2, Finance Stoch. 13 (2009), 445-469. (2009) Zbl1195.91152MR2519840DOI10.1007/s00780-009-0091-2

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.