Pricing Credit Default Swap under Fractional Vasicek Interest Rate Model

Affiliation(s)

Department of Applied Mathematics, Shanghai Finance University, Shanghai, China.

Department of Applied Mathematics, Shanghai Finance University, Shanghai, China; School of Business Information Management, Shanghai University of International Business and Economics, Shanghai, China.

Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, China.

Department of Applied Mathematics, Shanghai Finance University, Shanghai, China.

Department of Applied Mathematics, Shanghai Finance University, Shanghai, China; School of Business Information Management, Shanghai University of International Business and Economics, Shanghai, China.

Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, China.

ABSTRACT

This paper discusses the pricing problem of credit default swap in the fractional Brownian motion environment. As credit default swap is exposed to both the interest rate risk and the default risk, we assume that the default intensity of a firm depends on the stochastic interest rate and the default states of counterparty firms. The interest rate risk is reflected by the fractional Vasicek interest rate model. We model the firm’s default intensity under the looping default model and derive the pricing formulas of risky bonds and credit default swap.

KEYWORDS

Credit Default Swap; Bond; Contagious Risk; Fractional Vasicek Interest Rate Model; Looping Default

Credit Default Swap; Bond; Contagious Risk; Fractional Vasicek Interest Rate Model; Looping Default

Cite this paper

R. Hao, Y. Liu and S. Wang, "Pricing Credit Default Swap under Fractional Vasicek Interest Rate Model,"*Journal of Mathematical Finance*, Vol. 4 No. 1, 2014, pp. 10-20. doi: 10.4236/jmf.2014.41002.

R. Hao, Y. Liu and S. Wang, "Pricing Credit Default Swap under Fractional Vasicek Interest Rate Model,"

References

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http://dx.doi.org/10.1111/j.1540-6261.1995.tb05167.x

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http://dx.doi.org/10.1007/BF01531332

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[6] L. Decreusefond and A. S. Ustunel, “Stochastic Analysis of the Fractional Brownian Motion,” Potential Analysis, Vol. 10, 1999, pp. 177-214. http://dx.doi.org/10.1023/A:1008634027843

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http://dx.doi.org/10.1111/1467-9965.00025

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http://dx.doi.org/10.1137/S036301299834171X

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[10] Y. Hu and B. Oksendal, “Fractional White Noise Calculus and Application to Finance,” Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 6, No. 1, 2003, pp. 1-32.

[11] W. L. Huang, X. X. Tao and S. H. Li, “Pricing Formulae for European Option under the Fractional Vasicek Interest Rate Model,” Acta Mathematica Sinica (in Chinese), Vol. 55, No. 2, 2012, pp. 219-230.

[12] M. Davis and V. Lo, “Infectious Defaults,” Quantitive Finance, Vol. 1, No. 4, 1999, pp. 382-387.

http://dx.doi.org/10.1080/713665832

[13] R. A. Jarrow and F. Yu, “Counterparty Risk and the Pricing of Defaultable Securities,” Journal of Finance, Vol. 56, No. 5, 2001, pp. 1765-1799. http://dx.doi.org/10.1111/0022-1082.00389

[14] S. Y. Leung and Y. K. Kwork, “Credit Default Swap Valuation with Counterparty Risk,” Kyoto Economic Review, Vol. 74, No. 1, 2005, pp. 25-45.

[15] Y. F. Bai, X. H. Hu and Z. X. Ye, “A Model for Dependent Default with Hyperbolic Attenuation Effect and Valuation of Credit Default Swap,” Applied Mathematics and Mechanics (English Edition), Vol. 28, No. 12, 2007, pp. 1643-1649.

http://dx.doi.org/10.1007/s10483-007-1211-9

[16] R. L. Hao and Z. X. Ye, “The Intensity Model for Pricing Credit Securities with Jumpdiffusion and Counterparty Risk,” Mathematical Problems in Engineering, Vol. 10, 2011, pp. 1-16.

[17] R. L. Hao and Z. X. Ye, “Pricing CDS with Jump-Diffusion Risk in the Intensity-Based Model,” Advances in Intelligent and Soft Computing, Vol. 100, 2011, pp. 221-229. http://dx.doi.org/10.1007/978-3-642-22833-9_26

[1] R. A. Jarrow and S. M. Turnbull, “Pricing Derivatives on Financial Securities Subject to Credit risk,” Journal of Finance, Vol. 50, No. 1, 1995, pp. 53-85.

http://dx.doi.org/10.1111/j.1540-6261.1995.tb05167.x

[2] J. D. Duffie and K. J. Singleton, “Modeling Term Structures of Defaultable Bonds,” Review of Financial Studies, Vol. 12, No. 4, 1999, pp. 687-720. http://dx.doi.org/10.1093/rfs/12.4.687

[3] D. Lando, “On Cox processes and credit risky securities,” The Review Derivatives Research, Vol. 2, No. 2, 1998, pp. 99-120.

http://dx.doi.org/10.1007/BF01531332

[4] D. Duffie, et al., “Transform Analysis and Asset Pricing for Affine Jump Diffusions,” Econometrica, Vol. 68, No. 6, 2000, pp. 1343-1376. http://dx.doi.org/10.1111/1468-0262.00164

[5] S. J. Lin, “Stochastic Analysis of Fractional Brownian Motion, Fractional Noises and Applications,” SIAM Review, Vol. 10, 1995, pp. 422-437.

[6] L. Decreusefond and A. S. Ustunel, “Stochastic Analysis of the Fractional Brownian Motion,” Potential Analysis, Vol. 10, 1999, pp. 177-214. http://dx.doi.org/10.1023/A:1008634027843

[7] L. C. G. Rogers, “Arbitrage with Fractional Brownian Motion,” Mathematical Finance, Vol. 7, No. 1, 1997, pp. 95-105.

http://dx.doi.org/10.1111/1467-9965.00025

[8] T. E. Duncan, Y. Hu and B. Pasik-Duncan, “Stochastic Calculus for Fractional Brownian Motion, I. Theory,” SIAM Journal on Control and Optimization, Vol. 38, No. 2, 2000, pp. 582-612.

http://dx.doi.org/10.1137/S036301299834171X

[9] Y. Hu, B. Oksendal and A. Sulem, “Optimal Portfolio in a Fractional Black-Scholes Market,” In: S. Albeverio, et al., Eds, Mathematical Physics and Stochastic Analysis, World Scientific, Singapore City, 2000.

[10] Y. Hu and B. Oksendal, “Fractional White Noise Calculus and Application to Finance,” Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 6, No. 1, 2003, pp. 1-32.

[11] W. L. Huang, X. X. Tao and S. H. Li, “Pricing Formulae for European Option under the Fractional Vasicek Interest Rate Model,” Acta Mathematica Sinica (in Chinese), Vol. 55, No. 2, 2012, pp. 219-230.

[12] M. Davis and V. Lo, “Infectious Defaults,” Quantitive Finance, Vol. 1, No. 4, 1999, pp. 382-387.

http://dx.doi.org/10.1080/713665832

[13] R. A. Jarrow and F. Yu, “Counterparty Risk and the Pricing of Defaultable Securities,” Journal of Finance, Vol. 56, No. 5, 2001, pp. 1765-1799. http://dx.doi.org/10.1111/0022-1082.00389

[14] S. Y. Leung and Y. K. Kwork, “Credit Default Swap Valuation with Counterparty Risk,” Kyoto Economic Review, Vol. 74, No. 1, 2005, pp. 25-45.

[15] Y. F. Bai, X. H. Hu and Z. X. Ye, “A Model for Dependent Default with Hyperbolic Attenuation Effect and Valuation of Credit Default Swap,” Applied Mathematics and Mechanics (English Edition), Vol. 28, No. 12, 2007, pp. 1643-1649.

http://dx.doi.org/10.1007/s10483-007-1211-9

[16] R. L. Hao and Z. X. Ye, “The Intensity Model for Pricing Credit Securities with Jumpdiffusion and Counterparty Risk,” Mathematical Problems in Engineering, Vol. 10, 2011, pp. 1-16.

[17] R. L. Hao and Z. X. Ye, “Pricing CDS with Jump-Diffusion Risk in the Intensity-Based Model,” Advances in Intelligent and Soft Computing, Vol. 100, 2011, pp. 221-229. http://dx.doi.org/10.1007/978-3-642-22833-9_26