Higher Order Finite Difference Scheme for solving 3D Black-Scholes equation based on Generic Factored Approximate Sparse Inverse Preconditioning using Reordering Schemes
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Abstract
In the area of derivatives pricing, the key model for the theoretical evaluation of options is the Black-Scholes partial differential equation. In this paper we present a fourth order accurate discretization scheme in conjunction with Richardson extrapolation method, while for the time integration we consider high order implicit Backward Differences along with an implicit Runge-Kutta method for the numerical solution of the Black-Scholes equation in three space variables. The resulting sparse linear system is solved by the Preconditioned Biconjugate Gradient Stabilized (PBiCG-STAB) method, in conjunction with the Modified Generic Factored Approximate Sparse Inverse (MGenFAspI) scheme, based on approximate inverse sparsity patterns, using reordering schemes. Numerical results indicating the applicability along with discussions concerning the implementation issues of the proposed schemes are presented.
References
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Index Terms
- Higher Order Finite Difference Scheme for solving 3D Black-Scholes equation based on Generic Factored Approximate Sparse Inverse Preconditioning using Reordering Schemes
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Published In
October 2014
355 pages
ISBN:9781450328975
DOI:10.1145/2645791
- General Chairs:
- Katsikas Sokratis,
- Hatzopoulos Michael,
- Apostolopoulos Theodoros,
- Anagnostopoulos Dimosthenis,
- Program Chairs:
- Carayiannis Elias,
- Varvarigou Theodora,
- Nikolaidou Mara
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In-Cooperation
- Greek Com Soc: Greek Computer Society
- Univ. of Piraeus: University of Piraeus
- National and Kapodistrian University of Athens: National and Kapodistrian University of Athens
- Athens U of Econ & Business: Athens University of Economics and Business
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Association for Computing Machinery
New York, NY, United States
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Published: 02 October 2014
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