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Topics in Numerical Methods for Finance pp 95–113Cite as

The COS Method for Pricing Options Under Uncertain Volatility

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 19))

Abstract

We develop a method for pricing financial options under uncertain volatility. The method is based on the dynamic programming principle and a Fourier cosine expansion method. Local errors in the vicinity of domain boundaries, originating from the use of Fourier series expansions, may hamper the algorithm’s convergence. We use an extrapolation method to deal with these errors.

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Notes

  1. 1.

    The methodology above can also be applied if the approximated continuation value is inaccurate in a certain area [a, x  ∗ ∗ ].

References

  1. Boyd, J.P.: Chebyshev and Fourier Spectral Methods. Courier Dover Publications, New York (2001)

    MATH  Google Scholar 

  2. Crandall, M.G., Ishii, H., Lions, P.L.: A user’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. 27, 1–67 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Duffie, D., Pan, J., Singleton, K.J.: Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68(6), 1343–1376 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fang, F., Oosterlee, C.W.: A novel pricing method for European options based on Fourier-cosine series expansions. SIAM J. Sci. Comput. 31(2), 826–848 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fang, F., Oosterlee, C.W.: Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions. Numer. Math. 114(1), 27–62 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Forsyth, P.A., Labahn, G.: Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance. J. Comput. Finance 11(2), 1–44 (2007)

    Google Scholar 

  7. d’Halluin, Y., Forsyth, P.A., Vetzal, K.R.: Robust numerical methods for contingent claims under jump diffusion processes. IMA J. Numer. Anal. 25(1), 87–112 (2005)

    Google Scholar 

  8. Hull, J.C.: Options, Futures and Other Derivatives. Pearson/Prentice-Hall, New Jersey (2009)

    Google Scholar 

  9. Lions, P.L.: Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations part 2: viscosity solutions and uniqueness. Comm. Part. Differ. Equat. 8(11), 1229–1276 (1983)

    Article  MATH  Google Scholar 

  10. Pham, H.: Continuous-Time Stochastic Control and Optimization with Financial Applications. Springer-Verlag, Berlin (2009)

    Book  MATH  Google Scholar 

  11. Pooley, D.M., Forsyth, P.A., Vetzal, K.R.: Numerical convergence properties of option pricing PDEs with uncertain volatility. IMA J. Numer. Anal. 23(2), 241–267 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ruijter, M.J.: On the Fourier cosine series expansion (COS) method for stochastic control problems. Working paper (2011)

    Google Scholar 

  13. Zhang, K., Wong, S.: A computational scheme for uncertain volatility model in option pricing. 59(8), 1754–1767 (2009)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, The Netherlands

    M. J. Ruijter & C. W. Oosterlee

  2. CPB Netherlands Bureau for Economic Policy Analysis, Van Stolkweg 14, Den Haag, The Netherlands

    M. J. Ruijter

  3. Delft University of Technology, Mekelweg 4, Delft, The Netherlands

    C. W. Oosterlee

Authors
  1. M. J. Ruijter
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  2. C. W. Oosterlee
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Corresponding author

Correspondence to M. J. Ruijter .

Editor information

Editors and Affiliations

  1. , Dublin City Univ. Business School, Dublin City University, Ballymun Rd, Dublin 9, Dublin 9, Ireland

    Mark Cummins

  2. , Kemmy Business School, University of Limerick, Limerick, Ireland

    Finbarr Murphy

  3. Inst. for Numerical Computat. & Analy., 7 - 9 Dame Court, Dublin 2, Dublin 2, Ireland

    John J.H. Miller

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Ruijter, M.J., Oosterlee, C.W. (2012). The COS Method for Pricing Options Under Uncertain Volatility. In: Cummins, M., Murphy, F., Miller, J. (eds) Topics in Numerical Methods for Finance. Springer Proceedings in Mathematics & Statistics, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-3433-7_6

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