E-N. G. Grylonakis
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.
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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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