American Institute of Mathematical Sciences

Advanced
July  2017, 13(3): 1395-1415. doi: 10.3934/jimo.2016079

Pricing credit derivatives under a correlated regime-switching hazard processes model

Yinghui Dong 1,, , Kam Chuen Yuen 2, and  Guojing Wang 3,

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

* Corresponding author:Yinghui Dong

Received  February 2016 Published  October 2016

Fund Project: The authors thank the anonymous referees for valuable comments to improve the earlier version of the paper. The first author is supported by the NSF of Jiangsu Province (Grant No. BK20130260), the NNSF of China (Grant No. 11301369) and Qing Lan Project. The second author is supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7057/13P), and the CAE 2013 research grant from the Society of Actuaries -any opinions, finding, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the SOA. The third author is supported by the NNSF of China (Grant No. 11371274).

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.

Keywords: Hazard process, Markov chain, kth-to-default basket swap, multivariate regime-switching shot noise process.
Mathematics Subject Classification: Primary: 91B25, 91B70; Secondary: 60J27.
Citation: Yinghui Dong, Kam Chuen Yuen, Guojing Wang. Pricing credit derivatives under a correlated regime-switching hazard processes model. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1395-1415. doi: 10.3934/jimo.2016079
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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[14]

R. J. Elliott, L. Aggoun and J. B. Moore, Hidden Markov Models: Estimation and Control, Springer-Verlag: Berlin-Heidelberg-New York, 1995.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[19]

K. Giesecke and L. Goldberg, Sequential defaults and incomplete information, J. Risk, 7 (2004), 1-26.  doi: 10.21314/JOR.2004.100.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[14]

R. J. Elliott, L. Aggoun and J. B. Moore, Hidden Markov Models: Estimation and Control, Springer-Verlag: Berlin-Heidelberg-New York, 1995.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[19]

K. Giesecke and L. Goldberg, Sequential defaults and incomplete information, J. Risk, 7 (2004), 1-26.  doi: 10.21314/JOR.2004.100.  Google Scholar

[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.  Google Scholar

Figure 1.  Term structure of $s_1$ with $a=1$
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  Impact of $w$ on $s_1$ with $a=1, T=10.$
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  Impact of $a$ on $s_1$ with $w=0.01, T=10.$
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4.  Term structure of $s^1$ with $a=1$
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5.  Impact of $w$ on $s^1$ and with $q=0.5, T=10.$
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 6.  Impact of $a$ on $s^1$ and with $q=0.5, T=10.$
Figure Options

Download full-size image

Download as PowerPoint slide

[1]

Kun Fan, Yang Shen, Tak Kuen Siu, Rongming Wang. On a Markov chain approximation method for option pricing with regime switching. Journal of Industrial & Management Optimization, 2016, 12 (2) : 529-541. doi: 10.3934/jimo.2016.12.529
[2]

Jiaqin Wei, Zhuo Jin, Hailiang Yang. Optimal dividend policy with liability constraint under a hidden Markov regime-switching model. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1965-1993. doi: 10.3934/jimo.2018132
[3]

Fuke Wu, George Yin, Zhuo Jin. Kolmogorov-type systems with regime-switching jump diffusion perturbations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2293-2319. doi: 10.3934/dcdsb.2016048
[4]

Jiaqin Wei. Time-inconsistent optimal control problems with regime-switching. Mathematical Control & Related Fields, 2017, 7 (4) : 585-622. doi: 10.3934/mcrf.2017022
[5]

Zhuo Jin, Linyi Qian. Lookback option pricing for regime-switching jump diffusion models. Mathematical Control & Related Fields, 2015, 5 (2) : 237-258. doi: 10.3934/mcrf.2015.5.237
[6]

Mourad Bellassoued, Raymond Brummelhuis, Michel Cristofol, Éric Soccorsi. Stable reconstruction of the volatility in a regime-switching local-volatility model. Mathematical Control & Related Fields, 2020, 10 (1) : 189-215. doi: 10.3934/mcrf.2019036
[7]

Christoforidou Amalia, Christian-Oliver Ewald. A lattice method for option evaluation with regime-switching asset correlation structure. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2020042
[8]

Lin Xu, Rongming Wang, Dingjun Yao. Optimal stochastic investment games under Markov regime switching market. Journal of Industrial & Management Optimization, 2014, 10 (3) : 795-815. doi: 10.3934/jimo.2014.10.795
[9]

Zhuo Jin, George Yin, Hailiang Yang. Numerical methods for dividend optimization using regime-switching jump-diffusion models. Mathematical Control & Related Fields, 2011, 1 (1) : 21-40. doi: 10.3934/mcrf.2011.1.21
[10]

Jiapeng Liu, Ruihua Liu, Dan Ren. Investment and consumption in regime-switching models with proportional transaction costs and log utility. Mathematical Control & Related Fields, 2017, 7 (3) : 465-491. doi: 10.3934/mcrf.2017017
[11]

Chao Xu, Yinghui Dong, Zhaolu Tian, Guojing Wang. Pricing dynamic fund protection under a Regime-switching Jump-diffusion model with stochastic protection level. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-21. doi: 10.3934/jimo.2019072
[12]

Ping Chen, Haixiang Yao. Continuous-time mean-variance portfolio selection with no-shorting constraints and regime-switching. Journal of Industrial & Management Optimization, 2020, 16 (2) : 531-551. doi: 10.3934/jimo.2018166
[13]

Jui-Jung Tsai, Yang-Chao Wang, Jiarong Zhang. Measuring financial contagion between major european stock markets via the regime-switching vine copula model. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020267
[14]

Daoyi Xu, Yumei Huang, Zhiguo Yang. Existence theorems for periodic Markov process and stochastic functional differential equations. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 1005-1023. doi: 10.3934/dcds.2009.24.1005
[15]

Victor Meng Hwee Ong, David J. Nott, Taeryon Choi, Ajay Jasra. Flexible online multivariate regression with variational Bayes and the matrix-variate Dirichlet process. Foundations of Data Science, 2019, 1 (2) : 129-156. doi: 10.3934/fods.2019006
[16]

Yan Wang, Lei Wang, Yanxiang Zhao, Aimin Song, Yanping Ma. A stochastic model for microbial fermentation process under Gaussian white noise environment. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 381-392. doi: 10.3934/naco.2015.5.381
[17]

Tak Kuen Siu, Yang Shen. Risk-minimizing pricing and Esscher transform in a general non-Markovian regime-switching jump-diffusion model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2595-2626. doi: 10.3934/dcdsb.2017100
[18]

Lin Xu, Dingjun Yao, Gongpin Cheng. Optimal investment and dividend for an insurer under a Markov regime switching market with high gain tax. Journal of Industrial & Management Optimization, 2020, 16 (1) : 325-356. doi: 10.3934/jimo.2018154
[19]

Robert J. Elliott, Tak Kuen Siu. Stochastic volatility with regime switching and uncertain noise: Filtering with sub-linear expectations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 59-81. doi: 10.3934/dcdsb.2017003
[20]

Ummugul Bulut, Edward J. Allen. Derivation of SDES for a macroevolutionary process. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1777-1792. doi: 10.3934/dcdsb.2013.18.1777

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (37)
  • HTML views (359)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences