Volume 1, Issue 6
Fourth Order Compact Boundary Value Method for Option Pricing with Jumps

Spike T. Lee & Hai-Wei Sun

Adv. Appl. Math. Mech., 1 (2009), pp. 845-861.

Published online: 2009-01

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  • Abstract

We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential equation. Discretizing the spatial direction with a fourth order compact scheme leads to a linear system of ordinary differential equations. For the temporal direction, we utilize the favorable boundary value methods owing to their advantageous stability properties. In addition, the resulting large sparse system can be solved rapidly by the GMRES method with a circulant Strang-type preconditioner. Numerical results demonstrate the high order accuracy of our scheme and the efficiency of the preconditioned GMRES method.

  • Keywords

Partial integro-differential equation fourth order compact scheme boundary value method preconditioning Toeplitz matrix

  • AMS Subject Headings

65T50 65M06 65F10 91B28

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COPYRIGHT: © Global Science Press

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@Article{AAMM-1-845, author = {Spike T. Lee and Hai-Wei Sun}, title = {Fourth Order Compact Boundary Value Method for Option Pricing with Jumps}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {6}, pages = {845--861}, abstract = {

We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential equation. Discretizing the spatial direction with a fourth order compact scheme leads to a linear system of ordinary differential equations. For the temporal direction, we utilize the favorable boundary value methods owing to their advantageous stability properties. In addition, the resulting large sparse system can be solved rapidly by the GMRES method with a circulant Strang-type preconditioner. Numerical results demonstrate the high order accuracy of our scheme and the efficiency of the preconditioned GMRES method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m09S06}, url = {http://global-sci.org/intro/article_detail/aamm/8401.html} }
TY - JOUR T1 - Fourth Order Compact Boundary Value Method for Option Pricing with Jumps AU - Spike T. Lee & Hai-Wei Sun JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 845 EP - 861 PY - 2009 DA - 2009/01 SN - 1 DO - http://dor.org/10.4208/aamm.09-m09S06 UR - https://global-sci.org/intro/aamm/8401.html KW - Partial integro-differential equation KW - fourth order compact scheme KW - boundary value method KW - preconditioning KW - Toeplitz matrix AB -

We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential equation. Discretizing the spatial direction with a fourth order compact scheme leads to a linear system of ordinary differential equations. For the temporal direction, we utilize the favorable boundary value methods owing to their advantageous stability properties. In addition, the resulting large sparse system can be solved rapidly by the GMRES method with a circulant Strang-type preconditioner. Numerical results demonstrate the high order accuracy of our scheme and the efficiency of the preconditioned GMRES method.

Spike T. Lee & Hai-Wei Sun. (1970). Fourth Order Compact Boundary Value Method for Option Pricing with Jumps. Advances in Applied Mathematics and Mechanics. 1 (6). 845-861. doi:10.4208/aamm.09-m09S06
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