About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 960789, 13 pages
http://dx.doi.org/10.1155/2013/960789
Research Article

Valuation of the Prepayment Option of a Perpetual Corporate Loan

1BNP Paribas CIB Resource Portfolio Management and CEREMADE, Université Paris Dauphine, 75016 Paris, France
2CEREMADE, Université Paris Dauphine, 75016 Paris, France

Received 13 December 2012; Accepted 2 February 2013

Academic Editor: Dragoş-Pătru Covei

Copyright © 2013 Timothee Papin and Gabriel Turinici. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. Cossin and H. A. Lu, Pricing Prepayment Option in C & I Loans at Origination, University of Lausanne, School of Economics and Business Administration (HEC-Lausanne).
  2. G. G. Kaufman, T. H. Krueger, and W. C. Hunter, The Asian Financial Crisis: Origins, Implications and Solutions, Springer, 1999.
  3. B. Henry and J. Nixon, “The crisis in Russia: some initial observations,” Economic Outlook, vol. 23, no. 1, pp. 22–29, 1998. View at Publisher · View at Google Scholar
  4. J. B. Hillard, J. E. Kau, and V. C. Slawson, “Valuing prepayment and default in a fixed-rate mortgage: a bivariate binomial options pricing technique,” Real Estate Economic, vol. 26, no. 3, pp. 431–468, 1998.
  5. Y. Chen, M. Connolly, W. Tang, and T. Su, “The value of mortgage prepayment and default options,” Journal of Futures Markets, vol. 29, pp. 840–861, 2009.
  6. E. S. Schwartz and W. N. Torous, “Mortgage prepayment and default decisions: a poisson regression approach,” American Real Estate and Urban Economics Association, vol. 21, no. 4, pp. 431–449, 1993. View at Publisher · View at Google Scholar
  7. X. Guo and Q. Zhang, “Closed-form solutions for perpetual American put options with regime switching,” SIAM Journal on Applied Mathematics, vol. 64, no. 6, pp. 2034–2049, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. X. Guo, “An explicit solution to an optimal stopping problem with regime switching,” Journal of Applied Probability, vol. 38, no. 2, pp. 464–481, 2001. View at Publisher · View at Google Scholar
  9. Y. Xu and Y. Wu, “Perpetual American maximum options with Markov-modulated dynamics,” Lithuanian Mathematical Journal, vol. 51, no. 1, pp. 106–119, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  10. R. S. Mamon and M. R. Rodrigo, “Explicit solutions to European options in a regime-switching economy,” Operations Research Letters, vol. 33, no. 6, pp. 581–586, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Buffington and R. J. Elliott, “American options with regime switching,” International Journal of Theoretical and Applied Finance, vol. 5, pp. 497–514, 2009.
  12. A. Jobert and L. C. G. Rogers, “Option pricing with Markov-modulated dynamics,” SIAM Journal on Control and Optimization, vol. 44, no. 6, pp. 2063–2078, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. D. D. Yao, Q. Zhang, and X. Y. Zhou, “A regime-switching model for European options,” in Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, & Management Science2006, H. Yan, G. Yin, and Q. Zhang, Eds., vol. 94 of International Series in Operations ResearchQueueing Networks, and Manufacturing Systems, pp. 281–300, Springer.
  14. T. K. Siu, H. Yang, and J. W. Lau, “Pricing currency options under two-factor Markov-modulated stochastic volatility models,” Insurance: Mathematics and Economics, vol. 43, no. 3, pp. 295–2302, 2008. View at Publisher · View at Google Scholar
  15. R. J. Elliott and T. K. Siu, “On Markov-modulated exponential-affine bond price formulae,” Applied Mathematical Finance, vol. 16, no. 1, pp. 1–15, 2009.
  16. N. Zhou and R. Mamon, “An accessible implementation of interest rate models with markov-switching,” Expert Systems With Applications, vol. 39, no. 5, pp. 4679–4689, 2012. View at Publisher · View at Google Scholar
  17. Y. Huang, P. A. Forsyth, and G. Labahn, “Methods for pricing American options under regime switching,” SIAM Journal on Scientific Computing, vol. 33, no. 5, pp. 2144–2168, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. P. Jaillet, D. Lamberton, and B. Lapeyre, “Variational inequalities and the pricing of American options,” Acta Applicandae Mathematicae, vol. 21, no. 3, pp. 263–289, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. J. C. Cox, J. E. Ingersoll, and S. A. Ross, “A theory of the term structure of interest rates,” Econometrica, vol. 53, no. 2, pp. 385–407, 1985. View at Publisher · View at Google Scholar
  20. A. Aurélien, “On the discretization schemes for the CIR, (and Bessel squared) processes,” Monte Carlo Methods and Applications, vol. 11, no. 4, pp. 355–384, 2005. View at Publisher · View at Google Scholar
  21. D. Lamberton and B. Lapeyre, Introduction To sTochastic Calculus Applied To Finance, Chapman & Hall/ CRC, 2nd edition, 2008.
  22. D. Lando, Credit Risk Modeling, Princeton University Press, Princeton, NJ, USA, 2004.
  23. B. Øksendal, Stochastic Differential Equations, Universitext, Springer, Berlin, Germany, 6 edition, 2007.
  24. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, Dover, New York, NY, USA, 9th-10th edition, 1964.
  25. M. Musiela and M. Rutkowski, Martingale Methods in Financial Modelling, Springer, 2005.
  26. R. Myneni, “The pricing of the American option,” The Annals of Applied Probability, vol. 2, no. 2, pp. 1–23, 1992. View at Publisher · View at Google Scholar
  27. A. Bensoussan, “On the theory of option pricing,” Acta Applicandae Mathematicae, vol. 2, no. 2, pp. 139–158, 1984. View at Zentralblatt MATH · View at MathSciNet
  28. M. Chesney, R. J. Elliott, and R. Gibson, “Analytical solutions for the pricing of American bond and yield options,” Mathematical Finance, vol. 3, pp. 277–294, 1993.