Bergische Universität Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Angewandte Mathematik - Numerische Analysis

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ADE, ADI and LOD Splitting Methods for Option Pricing


Masterarbeit Wirtschaftsmathematik


Master's Thesis in Financial Mathematics, Halmstad University, Sweden



Supervision


Description

In this thesis we discuss ...

Keywords

ADE splitting, ADI method, LOD method, Ikonen-Toivanen splitting

References:

  1. R.M. Beam, R.F. Warming, Alternating Direction Implicit Methods for Parabolic Equations with a Mixed Derivative, SIAM J. Sci. Stat. Comput. 1 (1980), 131-159.
  2. D.M. Dang, C. Christara, K.R. Jackson, A Parallel Implementation on GPUs of ADI Finite Difference Methods for Parabolic PDEs with Applications in Finance, (2010), .
  3. D.J. Duffy, Unconditionally Stable and Second-Order Accurate Explicit Finite Difference Schemes Using Domain Transformation: Part I One-Factor Equity Problems, (2009), SSRN.
  4. K. in 't Hout, C. Mishra, Stability of the Modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with mixed derivative term, Submitted for publication (2010).
  5. T. Haentjens, K. in 't Hout, K. Volders, ADI schemes with Ikonen-Toivanen splitting for pricing American put options in the Heston model, In: T.E. Simos et. al. (eds.), Numerical Analysis and Applied Mathematics, AIP Conf. Proc. 1281 (2010), 231-234.
  6. T. Haentjens, K. in 't Hout, ADI finite difference discretization of the Heston-Hull-White PDE, In: T.E. Simos et. al. (eds.), Numerical Analysis and Applied Mathematics, AIP Conf. Proc. 1281 (2010), 1995-1999.
  7. K. in 't Hout, C. Mishra, A stability result for the Modified Craig-Sneyd scheme applied to 2D and 3D pure diffusion equations, In: T.E. Simos et. al. (eds.), Numerical Analysis and Applied Mathematics, AIP Conf. Proc. 1281 (2010), 2029-2032.
  8. K. in 't Hout, S. Foulon: ADI finite difference schemes for option pricing in the Heston model with correlation, Int. J. Numer. Anal. Mod. 7 (2010), 303-320.
  9. K. in 't Hout, B.D. Welfert, Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms, Appl. Numer. Math. 59 (2009), 677-692.
  10. K. in 't Hout, ADI schemes in the numerical solution of the Heston PDE, In: T.E. Simos et. al. (eds.), Numerical Analysis and Applied Mathematics, AIP Conf. Proc. 936 (2007), 10-14.
  11. S. Leung, S. Osher, Alternating Direction Explicit (ADE) Scheme for Time-Dependent Evolution Equations, Preprint UCLA, June 2005.
  12. A.R. Mitchell, D.F. Griffiths. The Finite Difference Method in Partial Differential Equations, John Wiley & Sons, Inc., Chichester, 1980.
  13. P.W. Peaceman, H.H. Rachford, The numerical solution of Parabolic and Elliptic differential equation, J. Soc. Ind. Appl. Math. 3 (1955), 28-42.
  14. G. Pealat, D.J. Duffy, The Alternating Direction Explicit (ADE) Method for One-Factor Problems, Wilmott Magazine (2011), .
  15. S. Villeneuve, A. Zanette, Parabolic A.D.I. methods for pricing American options on two stocks, Math. Oper. Research. 27 (2002), 121-149.
  16. S. Villeneuve, A. Zanette, Comparison of Finite Difference Methods for Pricing American options on two stocks, (2009).
  17. N.N. Yanenko, The Method of Fractional Steps, Springer-Verlag, Berlin, 1971.


University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics
Applied Mathematics & Numerical Analysis Group

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