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A Fitted Multi-point Flux Approximation Method for Pricing Two Options

  • Rock Stephane Koffi
  • Antoine TambueEmail author
Article

Abstract

In this paper, we develop novel numerical methods based on the multi-point flux approximation (MPFA) method to solve the degenerated partial differential equation (PDE) arising from pricing two-assets options. The standard MPFA is used as our first method and is coupled with a fitted finite volume in our second method to handle the degeneracy of the PDE and the corresponding scheme is called fitted MPFA method. The convection part is discretized using the upwinding methods (first and second order) that we have derived on non uniform grids. The time discretization is performed with \(\theta \)-Euler methods. Numerical simulations show that our new schemes can be more accurate than the current fitted finite volume method proposed in the literature.

Keywords

Finite volume methods Multi-point flux approximation Degenerated PDEs Options pricing Multi-asset options 

Notes

Acknowledgements

This work was supported by the Robert Bosch Stiftung through the AIMS ARETE Chair programme (Grant No 11.5.8040.0033.0).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Western Norway University of Applied SciencesBergenNorway
  2. 2.The African Institute for Mathematical Sciences(AIMS)MuizenbergSouth Africa
  3. 3.Center for Research in Computational and Applied Mechanics (CERECAM)University of Cape TownRondeboschSouth Africa
  4. 4.Department of Mathematics and Applied MathematicsUniversity of Cape TownRondeboschSouth Africa

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