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Serial and Parallel Krylov Methods for Implicit Finite Difference Schemes Arising in Multivariate Option Pricing

Evis Këllezi, and Giorgio Pauletto ()
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Evis Këllezi,: University of Geneva and FAME

FAME Research Paper Series from International Center for Financial Asset Management and Engineering

Abstract: This paper investigates computational and implementation issues for the valuation of options on three underlying assets, focusing on the use of the finite difference methods. We demonstrate that implicit methods, which have good convergence and stability prooperties, can now be implemented efficiently due to the recent development of techniques that allow the efficient solution of large and sparse linear systems. In the trivariate option valuation problem, we use nonstationary iterative methods (also called Krylov methods) for the solution of the large and sparse linear systems arising while using implicit methods. Krylov methods are investigated both in serial and in parallel implementations. Computational results show that the parallel implementation is particularly efficient if a fine grid space is needed.

Keywords: Multivariate option pricing, finite difference methods; Krylov methods; parallel Krylov methods (search for similar items in EconPapers)
JEL-codes: C63 C88 G13 (search for similar items in EconPapers)
Date: 2001-03
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