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Section B

Boundary value methods with the Crank–Nicolson preconditioner for pricing options in the jump-diffusion model

, &
Pages 1730-1748 | Received 06 Jan 2010, Accepted 13 Sep 2010, Published online: 14 Mar 2011

References

  • Almendral , A. and Oosterlee , C. 2005 . Numerical valuation of options with jumps in the underlying . Appl. Numer. Math. , 53 : 1 – 18 .
  • Bertaccini , D. 2000 . A circulant preconditioner for the systems of LMF-based ODE codes . SIAM J. Sci. Comput. , 22 : 767 – 786 .
  • Black , F. and Scholes , M. 1973 . The pricing of options and corporate liabilities . J. Polit. Economy , 81 : 637 – 654 .
  • Brugnano , L. and Trigiante , D. 1998 . Solving Differential Problems by Multistep Initial and Boundary Value Methods , Amsterdam : Gordan and Breach .
  • Chan , R. and Ng , M. 1996 . Conjugate gradient methods for Toeplitz systems . SIAM Rev. , 38 : 427 – 482 .
  • Chan , R. and Jin , X. 2007 . An Introduction to Iterative Toeplitz Solvers , Philadelphia, PA : SIAM .
  • Chan , R. , Ng , M. and Jin , X. 2001 . Strang-type preconditioners for systems of LMF-based ODE codes . IMA J. Numer. Anal. , 21 : 451 – 462 .
  • d'Halluin , Y. , Forsyth , P. and Vetzal , K. 2005 . Robust numerical methods for contingent claims under jump diffusion processes . IMA J. Numer. Anal. , 25 : 87 – 112 .
  • Feng , L. and Linetsky , V. 2008 . Pricing options in jump-diffusion models: An extrapolation approach . Oper. Res. , 56 : 304 – 325 .
  • Giles , M. and Carter , R. 2006 . Convergence analysis of Crank–Nicolson and Rannacher time-marching . J. Comput. Finance , 9 : 89 – 112 .
  • Hou , J. and Sun , H. 2008 . “ A preconditioner from Crank–Nicolson scheme for systems of LMF-based ODE code ” . In Recent Advances in Computational Mathematics , Edited by: Ding , D. , Jin , X.-Q. and Sun , H.-W. 139 – 149 . Somerville, MA : Higher Education Press, Beijing & International Press of Boston .
  • Karaa , S. and Zhang , J. 2004 . High order ADI method for solving unsteady convection-diffusion problems . J. Comput. Phys. , 198 : 1 – 9 .
  • Kou , S. 2002 . A jump-diffusion model for option pricing . Manag. Sci. , 48 : 1086 – 1101 .
  • Lee , S. and Sun , H. 2009 . Fourth order compact boundary value method for option pricing with jumps . Adv. Appl. Math. Mech. , 1 : 845 – 861 .
  • Merton , R. 1976 . Option pricing when underlying stock returns are discontinuous . J. Financ. Econ. , 3 : 125 – 144 .
  • Rannacher , R. 1984 . Finite element solution of diffusion problems with irregular data . Numer. Math. , 43 : 309 – 327 .
  • Saad , Y. 2000 . Iterative Methods for Sparse Linear Systems , 2 , Philadelphia, PA : SIAM .
  • Tangman , D. , Gopaul , A. and Bhuruth , M. 2008 . Numerical pricing of options using high-order compact finite difference schemes . J. Comput. Appl. Math. , 218 : 270 – 280 .
  • Tavella , D. and Randall , C. 2000 . Pricing Financial Instruments: The Finite Difference Method , New York : John Wiley and Sons .
  • Wilmott , P. 1998 . Derivatives: The Theory and Practice of Financial Engineering , West Sussex : John Wiley and Sons Ltd .
  • Zhang , J. , Sun , H. and Zhao , J. 2002 . High order compact scheme with multigrid local mesh refinement procedure for convection diffusion problems . Comput. Methods Appl. Mech. Eng. , 191 : 4661 – 4674 .

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