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Modelling the evolution of credit spreads using the Cox process within the HJM framework: A CDS option pricing model

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  • Chiarella, Carl
  • Fanelli, Viviana
  • Musti, Silvana

Abstract

In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provides the defaultable bond and credit default swap option price in a probability setting equipped with a subfiltration structure. The Euler-Maruyama stochastic integral approximation and the Monte Carlo method are applied to develop a numerical scheme for pricing. Finally, the antithetic variable technique is used to reduce the variance of credit default swap option prices.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 208 (2011)
Issue (Month): 2 (January)
Pages: 95-108

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Handle: RePEc:eee:ejores:v:208:y:2011:i:2:p:95-108

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Keywords: Pricing HJM model Cox process Monte Carlo method CDS option;

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References

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  1. Chiarella, Carl & Clewlow, Les & Musti, Silvana, 2005. "A volatility decomposition control variate technique for Monte Carlo simulations of Heath Jarrow Morton models," European Journal of Operational Research, Elsevier, Elsevier, vol. 161(2), pages 325-336, March.
  2. Jarrow, Robert A & Lando, David & Turnbull, Stuart M, 1997. "A Markov Model for the Term Structure of Credit Risk Spreads," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 481-523.
  3. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, vol. 50(1), pages 53-85, March.
  4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-70, May.
  5. Viviana Fanelli & Silvana Musti, 2007. "Modelling Credit Spreads evolution using the Cox Process within the HJM framework," Quaderni DSEMS, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia 27-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
  6. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, Econometric Society, vol. 69(3), pages 633-64, May.
  7. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
  8. Chen, Ren-Raw & Cheng, Xiaolin & Fabozzi, Frank J. & Liu, Bo, 2008. "An Explicit, Multi-Factor Credit Default Swap Pricing Model with Correlated Factors," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 43(01), pages 123-160, March.
  9. Jarrow, Robert A., 2008. "Operational risk," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 870-879, May.
  10. Farshid Jamshidian, 2004. "Valuation of credit default swaps and swaptions," Finance and Stochastics, Springer, vol. 8(3), pages 343-371, 08.
  11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  12. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
  13. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 77-105, January.
  14. Chunsheng Zhou, 1997. "A jump-diffusion approach to modeling credit risk and valuing defaultable securities," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 1997-15, Board of Governors of the Federal Reserve System (U.S.).
  15. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-67, May.
  16. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 2000. "A Discrete-Time Approach to Arbitrage-Free Pricing of Credit Derivatives," Management Science, INFORMS, INFORMS, vol. 46(1), pages 46-62, January.
  17. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
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Citations

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Cited by:
  1. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos Sklibosios, 2013. "Credit Derivatives Pricing With Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1350019-1-1.
  2. Moreno, Manuel & Serrano, Pedro & Stute, Winfried, 2011. "Statistical properties and economic implications of jump-diffusion processes with shot-noise effects," European Journal of Operational Research, Elsevier, Elsevier, vol. 214(3), pages 656-664, November.
  3. Mitra, Sovan & Date, Paresh & Mamon, Rogemar & Wang, I-Chieh, 2013. "Pricing and risk management of interest rate swaps," European Journal of Operational Research, Elsevier, Elsevier, vol. 228(1), pages 102-111.

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