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The Pricing of Total Return Swap Under Default Contagion Models with Jump-Diffusion Interest Rate Risk

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Abstract

In this paper, we consider a two-firm default contagion model with counterparty risk and jumpdiffusion interest rate risk. Under this model, we study the pricing of total return swap(TRS). We assume that the interest rate follows the Vasicek jump-diffusion model, and obtain the Libor market interest rate. The case that default is related to the interest rate is considered. Using the method of change of measure and the properties of conditional expectations, the joint conditional survival probability and joint conditional density function are derived. Applying the arbitragefree pricing principle of TRS in the complete market, we price the swap rate of TRS and obtain the closed-form solution. And we analyze the effect of various factors on the price of TRS.

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References

  1. R. Merton, On the pricing of corporate debt: The risk structure of interest rates, J. Finance, 29 (1974), 449–470.

    Google Scholar 

  2. F. Black and J. Cox, Valuing corporate securities: Some effects of bond indenture provisions, J. Finance, 31 (1976), 351–367.

    Article  Google Scholar 

  3. R. Geske, The valuation of corporate liabilities as compound options, J. Financial Quant. Anal., 12 (1977), 541–552.

    Article  Google Scholar 

  4. P. Artzner and F. Delbaen, Default risk insurance and incomplete markets, Math. Finance, 5 (1995), 187–195.

    Article  Google Scholar 

  5. D. Duffie, M. Schroder, and C. Skiadas, Recursive valuation of defaultable securities and the timing of resolution of uncertainty, Ann. Appl. Prob., 6 (1996), 1075–1090.

    Article  MathSciNet  Google Scholar 

  6. R. Jarrow and S. Turnbull, Pricing options on financial securities subject to default risk, J. Finance, 50 (1995), 53–86.

    Article  Google Scholar 

  7. D. Madan and H. Unal, Pricing the risk of default, Rev. Derivat. Res., 2 (1995), 121–160.

    MATH  Google Scholar 

  8. D. Duffie and D. Lando, The term structure of credit spreads with incomplete accounting information, Econometrica, 69 (2001), 633–664.

    Article  MathSciNet  Google Scholar 

  9. R. Jarrow and F. Yu, Counterparty risk and the pricing of defaultable securities, Journal of Finance, 56 (2001), 1765–1799.

    Article  Google Scholar 

  10. Y. Bai, X. Hu, and Z. Ye, A model for dependent default with hyperbolic attenuation effect and valuation of credit default swap, Applied Mathematics and Mechanics, 12 (2007), 1643–1649.

    Article  Google Scholar 

  11. R. Elliott, M. Jeablanc, and M. Yor, On models of default risk, Math. Finance, 10 (2000), 179–195.

    Article  MathSciNet  Google Scholar 

  12. F. Jamshidian, Valuation of credit default swaps and swaptions, Finance & Stochastics, 8(3) (2004), 343–371.

    Article  MathSciNet  Google Scholar 

  13. S. Y. Leung and Y. K. Kwok, Credit default swap valuation with counterparty risk, The Kyoto Economic Review, 74 (2005), 25–45.

    Google Scholar 

  14. A. Wang and Z. Ye, Credit risky securities valuation under a contagion model with interacting intensities, Journal of Applied Mathematics, 2011 (2011) Article ID 158020, 20 pages. doi:https://doi.org/10.1155/2011/158020.

    MathSciNet  MATH  Google Scholar 

  15. A. J. Wang and Z. X. Ye, The pricing of credit risky securities under stochastic interest rate model with default correlation, Applications of Mathematics, 58(6) (2013), 703–727.

    Article  MathSciNet  Google Scholar 

  16. A. Wang and Z. Ye, Total return swap valuation with counterparty risk and interest rate risk, Abstract and Applied Analysis, 2014 (2014), Article ID 412890, 12 pages.

    MathSciNet  MATH  Google Scholar 

  17. G. Chacko and S. Das, Pricing interest rate derivatives: A general approach, Review of Financial Studies, 15(1) (2002), 195–241.

    Article  Google Scholar 

  18. Z. Ye and R. Zhuang, Total return swap valuation, Journal of Applied Probability and Statistics, 28(1) (2012), 79–86.

    MathSciNet  MATH  Google Scholar 

  19. S. Das and R. Sundaram, An integrated model for hybrid securities, Management Science, 53(9) (2007), 1439–1451.

    Article  Google Scholar 

  20. M. Harrison and D. Kreps, Martingales and arbitrage in multi-period securities markets, Journal of Economic Theory, 20 (1979), 381–408.

    Article  MathSciNet  Google Scholar 

  21. M. Harrison and Stanley Pliska, Martinggales and stochastic integrals in the theory of continuous trading, Stochatic Processes and Their Applications, 11 (1981), 215–260.

    Article  Google Scholar 

  22. R. L. Hao and Z. X. Ye, The intensity model for pricing credit securities with jump diffusion and counterparty risk, Mathematical Problems in Engineering, 2011 (2011), Article ID 412565, 16 pages.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Shanghai University of International Business and Economics, Shanghai, 201620, China

    Anjiao Wang

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  1. Anjiao Wang
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Correspondence to Anjiao Wang.

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Wang, A. The Pricing of Total Return Swap Under Default Contagion Models with Jump-Diffusion Interest Rate Risk. Indian J Pure Appl Math 51, 361–373 (2020). https://doi.org/10.1007/s13226-020-0405-9

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  • DOI: https://doi.org/10.1007/s13226-020-0405-9

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