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

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  • Evis KËLLEZI,

    (University of Geneva and FAME)

  • Giorgio PAULETTO

    (University of Geneva)

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.

Suggested Citation

  • Evis KËLLEZI, & Giorgio PAULETTO, 2001. "Serial and Parallel Krylov Methods for Implicit Finite Difference Schemes Arising in Multivariate Option Pricing," FAME Research Paper Series rp30, International Center for Financial Asset Management and Engineering.
  • Handle: RePEc:fam:rpseri:rp30
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    File URL: http://www.swissfinanceinstitute.ch/rp30.pdf
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    Keywords

    Multivariate option pricing; finite difference methods; Krylov methods; parallel Krylov methods;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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