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Wavelet Methods in PDE Valuation of Financial Derivatives

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Intelligent Data Engineering and Automated Learning — IDEAL 2000. Data Mining, Financial Engineering, and Intelligent Agents (IDEAL 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1983))

Abstract

We investigate the application of a wavelet method of lines solution method to financial PDEs. We demonstrate the suitability of a numerical scheme based on biorthogonal interpolating wavelets to financial PDE problems where there are discontinuities or regions of sharp transitions in the solution. The examples treated are the Black Scholes PDE with discontinuous payoffs and a 3-dimensional cross currency swap PDE for which a speedup over standard finite difference methods of two orders of magnitude is reported.

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References

  1. Beylkin, G. (1993). Wavelets and fast numerical algorithms. Lecture Notes for Short Course, AMS 93.

    Google Scholar 

  2. Beylkin, G., R. Coifman and V. Rokhlin (1991). Fast wavelet transforms and numerical algorithms. Comm. Pure and Appl. Math 44 141–183.

    Article  MATH  MathSciNet  Google Scholar 

  3. Cohen, A., I. Daubechies and J. Feauveau (1992). Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl Math 45 485–560.

    Article  MATH  MathSciNet  Google Scholar 

  4. Cohen, A., S. Kaber, S. Muller and M. Postel (2000). Accurate adaptive multiresolution scheme for scalar conservation laws. Preprint, LAN University Paris.

    Google Scholar 

  5. Dahmen, W., S. Muller and T. Schlinkmann (1999). On a robust adaptive multigrid solver for convection-dominated problems. Technical report, RWTH Aachen. IGPM Report No 171.

    Google Scholar 

  6. Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia.

    Google Scholar 

  7. Dempster, M. A. H. and J. P. Hutton (1997). Numerical valuation of crosscurrency swaps and swaptions. In Mathematics of Derivative Securities, eds. M. A. H. Dempster and S. R. Pliska. Cambridge University Press, 473–503.

    Google Scholar 

  8. Deslauriers, G. and S. Dubuc (1989). Symmetric iterative interpolation processes. Constr. Approx 5 49–68.

    Article  MATH  MathSciNet  Google Scholar 

  9. Donoho, D. (1992). Interpolating wavelet tansforms. Presented at the NATO Advanced Study Institute conference, Ciocco, Italy.

    Google Scholar 

  10. Magee, B. (1999). Pay attention to interest. Risk (October) 67–71.

    Google Scholar 

  11. Polikar, R. The wavelet tutorial. http://www.public.iastate.edu/∼rpolikar/wavelet.html.

  12. Prosser, R. and R. Cant (1998). Evaluation of nonlinear terms using interpolating wavelets. Working paper, CFD laboratory, Department of Engineering, University of Cambridge.

    Google Scholar 

  13. Prosser, R. and R. Cant (1998). On the representation of derivatives using interpolating wavelets. Working paper, CFD laboratory, Department of Engineering, University of Cambridge.

    Google Scholar 

  14. Prosser, R. and R. Cant (1998). On the use of wavelets in computational combustion. Working paper, CFD laboratory, Department of Engineering, University of Cambridge.

    Google Scholar 

  15. Prosser, R. and R. Cant (1998). A wavelet-based method for the efficient simulation of combustion. J. Comp. Phys 147 (2) 337–361.

    Article  MATH  MathSciNet  Google Scholar 

  16. Schiesser, W. (1991). The Numerical Method of Lines. Academic Press, Inc.

    Google Scholar 

  17. Sweldens, W. (1996). Building your own wavelets at home. ACM SIGGRAPH Course Notes.

    Google Scholar 

  18. Vasilyev, O., D. Yuen and S. Paolucci (1996). A fast adaptive wavelet collocation algorithm for multi-dimensional PDEs. J. Comp. Phys 125 498–512.

    Article  MATH  Google Scholar 

  19. Vasilyev, O., D. Yuen and S. Paolucci (1997). Wavelets: an alternative approach to solving PDEs. Research Report, Supercomputer Institute, University of Minnesota.

    Google Scholar 

  20. Wilmott, P., S. Howison and J. Dewynne (1995). The Mathematics of Financial Derivatives. Cambridge University Press.

    Google Scholar 

  21. Xu, J. and W. Shann (1992). Galerkin-wavelet methods for two-point boundary value problems. Numerische Mathematik 63 123–144.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Centre for Financial Research Judge Institute of Management, University of Cambridge, UK

    M.A.H. Dempster, A. Eswaran & D.G. Richards

Authors
  1. M.A.H. Dempster
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  2. A. Eswaran
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  3. D.G. Richards
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong

    Kwong Sak Leung  & Lai-Wan Chan  & 

  2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

    Helen Meng

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© 2000 Springer-Verlag Berlin Heidelberg

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Dempster, M., Eswaran, A., Richards, D. (2000). Wavelet Methods in PDE Valuation of Financial Derivatives. In: Leung, K.S., Chan, LW., Meng, H. (eds) Intelligent Data Engineering and Automated Learning — IDEAL 2000. Data Mining, Financial Engineering, and Intelligent Agents. IDEAL 2000. Lecture Notes in Computer Science, vol 1983. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44491-2_32

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  • DOI: https://doi.org/10.1007/3-540-44491-2_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41450-6

  • Online ISBN: 978-3-540-44491-6

  • eBook Packages: Springer Book Archive

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