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Pricing credit derivatives under a correlated regime-switching hazard processes model
1. | Department of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China |
2. | Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong, China |
3. | Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou 215006, China |
In this paper, we study the valuation of a single-name credit default swap and a $k$th-to-default basket swap under a correlated regime-switching hazard processes model. We assume that the defaults of all the names are driven by a Markov chain describing the macro-economic conditions and some shock events modelled by a multivariate regime-switching shot noise process. Based on some expressions for the joint Laplace transform of the regime-switching shot noise processes, we give explicit formulas for the spread of a CDS contract and the $k$th-to-default basket swap.
References:
[1] |
C. Alexander and A. Kaeck, Regime dependent determinants of credit default swap spreads, J. Bank. Finan., 32 (2008), 1008-1021. Google Scholar |
[2] |
T. Bielecki, S. Crépey, M. Jeanblanc and B. Zargari, Valuation and hedging of CDS counterparty exposure in a Markov copula model,
Int. J. Theor. Appl. Finance, 15 (2012), 1250004, 39 pp.
doi: 10.1142/S0219024911006498. |
[3] |
D. Brigo, A. Pallavicini and R. Torresetti, Credit models and the crisis: Default cluster dynamics and the generalized Poisson loss model, J. Credit Risk, 6 (2010), 39-81. Google Scholar |
[4] |
J. Buffington and R. J. Elliott,
American options with regime switching, Int. J. Theor. Appl. Finance, 5 (2002), 497-514.
doi: 10.1142/S0219024902001523. |
[5] |
A. Dassios and J. Jang,
Pricing of catastrophe reinsurance & derivatives using the Cox process with shot noise intensity, Financ. Stoch, 7 (2003), 73-95.
doi: 10.1007/s007800200079. |
[6] |
M. Davis and V. Lo, Infectious defaults, Quant. Finance, 1 (2001), 382-387. Google Scholar |
[7] |
A. Davies,
Credit spread modeling with regime-switching techniques, J. Fixed Income, 14 (2004), 36-48.
doi: 10.3905/jfi.2004.461450. |
[8] |
G. Di Graziano and L. C. G. Rogers,
A dynamic approach to the modelling of correlation credit derivatives using Markov chains, Int. J. Theor. Appl. Finance, 12 (2009), 45-62.
doi: 10.1142/S0219024909005142. |
[9] |
X. W. Ding, K. Giesecke and P. I. Tomecek,
Time-changed birth processes and multiname credit derivatives, Oper. Res., 57 (2009), 990-1005.
doi: 10.1287/opre.1080.0652. |
[10] |
Y. H. Dong, K. C. Yuen and C. F. Wu,
Unilateral counterparty risk valuation of CDS using a regime-switching intensity model, Stat. Probabil. Lett., 85 (2014), 25-35.
doi: 10.1016/j.spl.2013.11.001. |
[11] |
Y. H. Dong, K. C. Yuen, G. J. Wang and C. F. Wu. A reduced-form model for correlated defaults with regime-switching shot noise intensities,
A reduced-form model for correlated defaults with regime-switching shot noise intensities, Methodol. Comput. Appl. Probab., 18 (2016), 459-486.
doi: 10.1007/s11009-014-9431-6. |
[12] |
D. Duffie and N. Gârleanu,
Risk and valuation of collateralized debt obligations, Financ. Anal. J., 57 (2001), 41-59.
doi: 10.2469/faj.v57.n1.2418. |
[13] |
D. Duffie, D. Filipovic and W. Schachermayer,
Affine processes and applications in finance, Ann. Appl. Probab., 13 (2003), 984-1053.
doi: 10.1214/aoap/1060202833. |
[14] |
R. J. Elliott, L. Aggoun and J. B. Moore,
Hidden Markov Models: Estimation and Control, Springer-Verlag: Berlin-Heidelberg-New York, 1995. |
[15] |
R. J. Elliott and T. K. Siu,
Default times in a continuous-time Markovian regime switching model, Stoch. Anal. Appl., 29 (2011), 824-837.
doi: 10.1080/07362994.2011.598792. |
[16] |
R. M. Gaspar and T. Schmidt, Credit risk modeling with shot-noise processes, working paper, 2010. Available from: http://ssrn.com/abstract=1588750. Google Scholar |
[17] |
K. Giesecke,
A simple exponential model for dependent defaults, J. Fixed Income, 13 (2003), 74-83.
doi: 10.2139/ssrn.315088. |
[18] |
K. Giesecke, F. A. Longstaff, S. Schaefer and I. Ilya Strebulaev,
Corporate bond default risk: A 150-year perspective, J. Financ. Econ., 102 (2011), 233-250.
doi: 10.1016/j.jfineco.2011.01.011. |
[19] |
K. Giesecke and L. Goldberg,
Sequential defaults and incomplete information, J. Risk, 7 (2004), 1-26.
doi: 10.21314/JOR.2004.100. |
[20] |
J. Hull and A. White, Valuation of a CDO and a nth to default CDS without Monte Carlo simulation, J. Derivatives, 12 (2004), 8-23. Google Scholar |
[21] |
R. Jarrow and F. Yu, Counterparty risk and the pricing of defaultable securities, J. Finan, 56 (2001), 1765-1799. Google Scholar |
[22] |
P. Schonbucher and D. Schubert, Copula dependent default risk in intensity models, Working Paper. Department of Statistics, Bonn University, 2001, Available from: http://ssrn.com/abstract=301968. Google Scholar |
[23] |
Y. Shen and T. K. Siu,
Longevity bond Pricing under stochastic interest rate and mortality with regime switching, Insur. Math. Econ., 52 (2013), 114-123.
doi: 10.1016/j.insmatheco.2012.11.006. |
show all references
References:
[1] |
C. Alexander and A. Kaeck, Regime dependent determinants of credit default swap spreads, J. Bank. Finan., 32 (2008), 1008-1021. Google Scholar |
[2] |
T. Bielecki, S. Crépey, M. Jeanblanc and B. Zargari, Valuation and hedging of CDS counterparty exposure in a Markov copula model,
Int. J. Theor. Appl. Finance, 15 (2012), 1250004, 39 pp.
doi: 10.1142/S0219024911006498. |
[3] |
D. Brigo, A. Pallavicini and R. Torresetti, Credit models and the crisis: Default cluster dynamics and the generalized Poisson loss model, J. Credit Risk, 6 (2010), 39-81. Google Scholar |
[4] |
J. Buffington and R. J. Elliott,
American options with regime switching, Int. J. Theor. Appl. Finance, 5 (2002), 497-514.
doi: 10.1142/S0219024902001523. |
[5] |
A. Dassios and J. Jang,
Pricing of catastrophe reinsurance & derivatives using the Cox process with shot noise intensity, Financ. Stoch, 7 (2003), 73-95.
doi: 10.1007/s007800200079. |
[6] |
M. Davis and V. Lo, Infectious defaults, Quant. Finance, 1 (2001), 382-387. Google Scholar |
[7] |
A. Davies,
Credit spread modeling with regime-switching techniques, J. Fixed Income, 14 (2004), 36-48.
doi: 10.3905/jfi.2004.461450. |
[8] |
G. Di Graziano and L. C. G. Rogers,
A dynamic approach to the modelling of correlation credit derivatives using Markov chains, Int. J. Theor. Appl. Finance, 12 (2009), 45-62.
doi: 10.1142/S0219024909005142. |
[9] |
X. W. Ding, K. Giesecke and P. I. Tomecek,
Time-changed birth processes and multiname credit derivatives, Oper. Res., 57 (2009), 990-1005.
doi: 10.1287/opre.1080.0652. |
[10] |
Y. H. Dong, K. C. Yuen and C. F. Wu,
Unilateral counterparty risk valuation of CDS using a regime-switching intensity model, Stat. Probabil. Lett., 85 (2014), 25-35.
doi: 10.1016/j.spl.2013.11.001. |
[11] |
Y. H. Dong, K. C. Yuen, G. J. Wang and C. F. Wu. A reduced-form model for correlated defaults with regime-switching shot noise intensities,
A reduced-form model for correlated defaults with regime-switching shot noise intensities, Methodol. Comput. Appl. Probab., 18 (2016), 459-486.
doi: 10.1007/s11009-014-9431-6. |
[12] |
D. Duffie and N. Gârleanu,
Risk and valuation of collateralized debt obligations, Financ. Anal. J., 57 (2001), 41-59.
doi: 10.2469/faj.v57.n1.2418. |
[13] |
D. Duffie, D. Filipovic and W. Schachermayer,
Affine processes and applications in finance, Ann. Appl. Probab., 13 (2003), 984-1053.
doi: 10.1214/aoap/1060202833. |
[14] |
R. J. Elliott, L. Aggoun and J. B. Moore,
Hidden Markov Models: Estimation and Control, Springer-Verlag: Berlin-Heidelberg-New York, 1995. |
[15] |
R. J. Elliott and T. K. Siu,
Default times in a continuous-time Markovian regime switching model, Stoch. Anal. Appl., 29 (2011), 824-837.
doi: 10.1080/07362994.2011.598792. |
[16] |
R. M. Gaspar and T. Schmidt, Credit risk modeling with shot-noise processes, working paper, 2010. Available from: http://ssrn.com/abstract=1588750. Google Scholar |
[17] |
K. Giesecke,
A simple exponential model for dependent defaults, J. Fixed Income, 13 (2003), 74-83.
doi: 10.2139/ssrn.315088. |
[18] |
K. Giesecke, F. A. Longstaff, S. Schaefer and I. Ilya Strebulaev,
Corporate bond default risk: A 150-year perspective, J. Financ. Econ., 102 (2011), 233-250.
doi: 10.1016/j.jfineco.2011.01.011. |
[19] |
K. Giesecke and L. Goldberg,
Sequential defaults and incomplete information, J. Risk, 7 (2004), 1-26.
doi: 10.21314/JOR.2004.100. |
[20] |
J. Hull and A. White, Valuation of a CDO and a nth to default CDS without Monte Carlo simulation, J. Derivatives, 12 (2004), 8-23. Google Scholar |
[21] |
R. Jarrow and F. Yu, Counterparty risk and the pricing of defaultable securities, J. Finan, 56 (2001), 1765-1799. Google Scholar |
[22] |
P. Schonbucher and D. Schubert, Copula dependent default risk in intensity models, Working Paper. Department of Statistics, Bonn University, 2001, Available from: http://ssrn.com/abstract=301968. Google Scholar |
[23] |
Y. Shen and T. K. Siu,
Longevity bond Pricing under stochastic interest rate and mortality with regime switching, Insur. Math. Econ., 52 (2013), 114-123.
doi: 10.1016/j.insmatheco.2012.11.006. |
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