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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 236091, 8 pages
http://dx.doi.org/10.1155/2014/236091
Research Article

Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market

1Department of Maths and Statistics, Curtin University, Perth, WA 6845, Australia
2School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
3School of Finance, Zhongnan University of Economics and Law, Wuhan 430073, China
4Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

Received 29 December 2013; Accepted 17 January 2014; Published 26 February 2014

Academic Editor: Yonghong Wu

Copyright © 2014 Shuang Li et al. 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. F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Political Economy, vol. 9, pp. 69–107, 1973.
  2. R. C. Merton, “Theory of rational option pricing,” The Rand Journal of Economics, vol. 4, pp. 141–183, 1973. View at MathSciNet
  3. S. Heston, “A closed-form solution for options with stochastic volatility with applications to bond and currency options,” Review of Financial Studies, vol. 6, no. 2, pp. 327–343, 1993.
  4. R. Merton, “Option pricing when underlying stock returns are discontinuous,” Journal of Financial Economics, vol. 3, no. 1, pp. 125–144, 1976.
  5. F. E. Benth and T. Meyer-Brandis, “The density process of the minimal entropy martingale measure in a stochastic volatility model with jumps,” Finance and Stochastics, vol. 9, no. 4, pp. 563–575, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  6. D. Bates, “The crash of ’87: was it expected? The evidence from options markets,” Journal of Finance, vol. 46, no. 3, pp. 1009–1044, 1991.
  7. J. Kallsen, “A utility maximization approach to hedging in incomplete markets,” Mathematical Methods of Operations Research, vol. 50, no. 2, pp. 321–338, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  8. T. Bielecki and M. Jeanblanc, Indifference Pricing of Defaultable Claims, Princeton University Press, 2004.
  9. J. Cvitanić, W. Schachermayer, and H. Wang, “Utility maximization in incomplete markets with random endowment,” Finance and Stochastics, vol. 5, no. 2, pp. 259–272, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  10. H. Föllmer and M. Schweizer, “Hedging of contingent claims under incomplete information,” in Applied Stochastic Analysis (London, 1989), vol. 5 of Stochastics Monographs, pp. 389–414, Gordon and Breach, New York, NY, USA, 1991. View at MathSciNet
  11. X. Ruan, W. Zhu, S. Li, and J. Huang, “Option pricing under risk-minimization criterion in an incomplete market with the finite difference method,” Mathematical Problems in Engineering, vol. 2013, Article ID 165727, 9 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  12. S. Ikonen and J. Toivanen, “Efficient numerical methods for pricing American options under stochastic volatility,” Numerical Methods for Partial Differential Equations, vol. 24, no. 1, pp. 104–126, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  13. D. Tavella and C. Randall, Pricing Financial Instruments: The Finite Difference Method, John Wiley and Sons, Chichester, UK, 2000.
  14. S. Salmi and J. Toivanen, “An iterative method for pricing American options under jump-diffusion models,” Applied Numerical Mathematics, vol. 61, no. 7, pp. 821–831, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  15. S. Ikonen and J. Toivanen, “Pricing American options using LU decomposition,” Applied Mathematical Sciences, vol. 1, no. 49–52, pp. 2529–2551, 2007. View at MathSciNet