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Mathematical Problems in Engineering
Volume 2017, Article ID 3912036, 8 pages
https://doi.org/10.1155/2017/3912036
Research Article

Efficient Simulation for Pricing Barrier Options with Two-Factor Stochastic Volatility and Stochastic Interest Rate

School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China

Correspondence should be addressed to Zhang Sumei; moc.anis@iemusggnahz

Received 11 August 2017; Accepted 8 October 2017; Published 14 November 2017

Academic Editor: Fazal M. Mahomed

Copyright © 2017 Zhang Sumei and Zhao Jieqiong. 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. R. Cont and P. Tankov, Financial Modelling with Jump Processes, Chapman & Hall, CRC Press, London, UK, 2004. View at MathSciNet
  2. P. Christoffersen, S. Heston, and K. Jacobs, “The shape and term structure of the index option smirk: why multifactor stochastic volatility models work so well,” Management Science, vol. 55, no. 12, pp. 1914–1932, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Yousuf, “A fourth-order smoothing scheme for pricing barrier options under stochastic volatility,” International Journal of Computer Mathematics, vol. 86, no. 6, pp. 1054–1067, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. M. Yousuf, “Efficient smoothing of Crank-Nicolson method for pricing barrier options under stochastic volatility,” PAMM, vol. 7, no. 1, pp. 1081101-1081102, 2007. View at Publisher · View at Google Scholar
  5. S. A. Griebsch and U. Wystup, “On the valuation of fader and discrete barrier options in Heston's stochastic volatility model,” Quantitative Finance, vol. 11, no. 5, pp. 693–709, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Y. Tian, Z. Zhu, F. C. Klebaner, and K. Hamza, “Pricing barrier and American options under the SABR model on the graphics processing unit,” Concurrency and Computation: Practice and Experience, vol. 24, no. 8, pp. 867–879, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. K. Shiraya, A. Takahashi, and T. Yamada, “Pricing discrete barrier options under stochastic volatility,” Asia-Pacific Financial Markets, vol. 19, no. 3, pp. 205–232, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. J. Jeon, J.-H. Yoon, and C.-R. Park, “An analytic expansion method for the valuation of double-barrier options under a stochastic volatility model,” Journal of Mathematical Analysis and Applications, vol. 449, no. 1, pp. 207–227, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. H. Funahashi and T. Higuchi, “An analytical approximation for single barrier options under stochastic volatility models,” Annals of Operations Research, vol. 6, pp. 1–29, 2017. View at Publisher · View at Google Scholar
  10. 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, no. 2, pp. 327–343, 1993. View at Publisher · View at Google Scholar
  11. J. Gatheral, The Volatility Surface: A Practitioner’s Guide, John Wiley & Sons, Inc., Hoboken, NJ, USA, 2012. View at Publisher · View at Google Scholar
  12. P. Gauthier and D. Possamai, “Efficient simulation of the double heston model,” IUP Journal of Computational Mathematics, vol. 4, no. 3, pp. 23–75, 2011. View at Publisher · View at Google Scholar
  13. A. Göncü and G. Ökten, “Efficient simulation of a multi-factor stochastic volatility model,” Journal of Computational and Applied Mathematics, vol. 259, no. 6, pp. 329–335, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  14. L. A. Grzelak, C. W. Oosterlee, and S. Van Weeren, “Extension of stochastic volatility equity models with the Hull-White interest rate process,” Quantitative Finance, vol. 12, no. 1, pp. 89–105, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. B. Chen, L. A. Grzelak, and C. W. Oosterlee, “Calibration and Monte Carlo pricing of the SABR-Hull-White model for long-maturity equity derivatives,” The Journal of Computational Finance, vol. 15, no. 4, pp. 79–113, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Guo, L. A. Grzelak, and C. W. Oosterlee, “Analysis of an affine version of the Heston-Hull-White option pricing partial differential equation,” Applied Numerical Mathematics, vol. 72, no. 1, pp. 143–159, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  17. S. Simaitis, C. S. de Graaf, N. Hari, and D. Kandhai, “Smile and default: the role of stochastic volatility and interest rates in counterparty credit risk,” Quantitative Finance, vol. 16, no. 11, pp. 1725–1740, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. C. Chiarella, B. Kang, and G. H. Meyer, “The evaluation of barrier option prices under stochastic volatility,” Computers & Mathematics with Applications, vol. 64, no. 6, pp. 2034–2048, 2012. View at Publisher · View at Google Scholar · View at Scopus
  19. Y. L. Hsiao, S. Y. Shen, and A. M. Wang, “A hybrid finite difference method for pricing two-asset double barrier options,” Mathematical Problems in Engineering, vol. 2015, Article ID 692695, 7 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  20. P. Shevchenko and P. Del Moral, “Valuation of barrier options using sequential Monte Carlo,” The Journal of Computational Finance, vol. 20, no. 4, pp. 107–135, 2016. View at Publisher · View at Google Scholar
  21. F. Cong and C. W. Oosterlee, “Multi-period mean-variance portfolio optimization based on Monte-Carlo simulation,” Journal of Economic Dynamics & Control, vol. 64, pp. 23–38, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  22. J. Hull and A. White, “Pricing interest-rate derivative securities,” Review of Financial Studies , vol. 3, no. 4, pp. 573–592, 1990. View at Publisher · View at Google Scholar
  23. D. Brigo and F. Mercurio, Interest Rate Models: Theory and Practice: With Smile, Inflation and Credit, Springer Finance, Springer, New York, NY, USA, 2nd edition, 2006. View at MathSciNet
  24. L. Andersen, “Efficient simulation of the Heston stochastic volatility model,” Journal of Computational Finance, vol. 11, no. 3, pp. 1–42, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  25. D. Dufresne, The Integrated Square-Root Process, Working paper, University of Montreal, 2001.
  26. P. Carr, M. Stanley, and D. B. Madan, “Option valuation using the fast Fourier transform,” The Journal of Computational Finance, vol. 2, no. 4, pp. 61–73, 1999. View at Publisher · View at Google Scholar
  27. S.-M. Zhang and L.-H. Wang, “A fast Fourier transform technique for pricing European options with stochastic volatility and jump risk,” Mathematical Problems in Engineering, vol. 2012, Article ID 761637, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. M. J. Wichura, “Algorithm AS 241: the percentage points of the normal distribution,” Journal of Applied Statistics, vol. 37, no. 3, pp. 477–484, 1988. View at Publisher · View at Google Scholar