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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 246724, 11 pages
http://dx.doi.org/10.1155/2013/246724
Research Article

Removing the Correlation Term in Option Pricing Heston Model: Numerical Analysis and Computing

Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain

Received 23 March 2013; Revised 18 May 2013; Accepted 20 May 2013

Academic Editor: T. Diagana

Copyright © 2013 R. Company 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. B. Dupire, “Arbitrage pricing with stochastic volatility,” Tech. Rep., Banque Paribas Swaps and Options Research Team Monograph, 1993.
  2. J. Hull and A. White, “The pricing of options with stochastic volatilities,” Journal of Finance, vol. 42, pp. 281–300, 1987.
  3. S. L. Heston, “A closed-form solution for options with stochastic volatility with applications to bond and currency options,” The Review of Financial Studies, vol. 6, pp. 327–343, 1993.
  4. P. Hagan, D. Kumar, and A. S. Lesniewski, “Managing smile risk,” Wilmott Magazine, vol. 15, pp. 84–108, 2002.
  5. A. Pascucci, PDE and Martingale Methods in Option Pricing, vol. 2 of Bocconi & Springer Series, Springer, Milan, Italy, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. Mikhailov and U. Nögel, “Heston's stochastic volatility model implementation, calibration and some extensions,” Wilmott Magazine, vol. 4, pp. 74–79, 2003.
  7. A. Elices, “Models with time-dependent parameters using transform methods: application to Heston's model,” http://arxiv.org/abs/0708.2020.
  8. E. Benhamou, E. Gobet, and M. Miri, “Time dependent Heston model,” SIAM Journal on Financial Mathematics, vol. 1, pp. 289–325, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. N. Hilber, A. M. Matache, and C. Schwab, “Sparse wavelet methods for option pricing under stochastic volatility,” Journal of Computational Finance, vol. 8, no. 4, pp. 1–42, 2005.
  10. W. Zhu and D. A. Kopriva, “A spectral element approximation to price European options with one asset and stochastic volatility,” Journal of Scientific Computing, vol. 42, no. 3, pp. 426–446, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. N. Clarke and K. Parrott, “Multigrid for american option pricing with stochastic volatility,” Applied Mathematical Finance, vol. 6, no. 3, pp. 177–195, 1999.
  12. R. Sheppard, Pricing equity derivatives under stochastic volatility: a partial differential equation approach [Ph.D. thesis], Faculty of Science, University of the Witwatersrand, 2007.
  13. B. Düring and M. Fournié, “High-order compact finite difference scheme for option pricing in stochastic volatility models,” Journal of Computational and Applied Mathematics, vol. 236, no. 17, pp. 4462–4473, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. D. J. Duffy, Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach, vol. 312, John Wiley & Sons, Chichester, UK, 2006. View at MathSciNet
  15. K. J. Hout and S. Foulon, “ADI finite difference schemes for option pricing in the Heston model with correlation,” International Journal of Numerical Analysis and Modeling, vol. 7, no. 2, pp. 303–320, 2010. View at MathSciNet
  16. R. Zvan, P. A. Forsyth, and K. R. Vetzal, “Negative coefficients in two-factor 25 option pricing models,” Journal of Computational Finance, vol. 7, no. 1, pp. 37–73, 2003.
  17. G. H. Golub and C. F. Van Loan, Matrix Computations, Johns Hopkins University Press, London, UK, 3rd edition, 1996. View at MathSciNet
  18. R. Company, L. Jódar, and J.-R. Pintos, “Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs,” Mathematical Modelling and Numerical Analysis, vol. 43, no. 6, pp. 1045–1061, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. R. Company, L. Jódar, and J.-R. Pintos, “Numerical analysis and computing for option pricing models in illiquid markets,” Mathematical and Computer Modelling, vol. 52, no. 7-8, pp. 1066–1073, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. M.-C. Casabán, R. Company, L. Jódar, and J.-R. Pintos, “Numerical analysis and computing of a non-arbitrage liquidity model with observable parameters for derivatives,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 1951–1956, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. P. R. Garabedian, Partial Differential Equations, AMS Chelsea, Providence, RI, USA, 1998. View at MathSciNet
  22. R. Ehrhardt, Discrete artificial boundary conditions [Ph.D. thesis], Technische Universitat Berlin, 2001.
  23. R. Kangro and R. Nicolaides, “Far field boundary conditions for Black-Scholes equations,” SIAM Journal on Numerical Analysis, vol. 38, no. 4, pp. 1357–1368, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. M. Ehrhardt and R. E. Mickens, “A fast, stable and accurate numerical method for the Black-Scholes equation of American options,” International Journal of Theoretical and Applied Finance, vol. 11, no. 5, pp. 471–501, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Clarendon Press, Oxford, UK, 3rd edition, 1985. View at MathSciNet