Lina Von Sydow | Uppsala University (original) (raw)
Address: Uppsala, Uppsala, Sweden
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Papers by Lina Von Sydow
Quaternary Science Reviews, Sep 1, 2016
arXiv (Cornell University), Aug 28, 2019
Applied Mathematical Finance, Mar 3, 2020
Mathematics and Computers in Simulation, 2020
Geoscientific Model Development, 2020
International Journal of Computer Mathematics, 2018
Journal of Computational Physics, 2017
Quantitative Finance, 2011
Computers & Mathematics With Applications - COMPUT MATH APPL, 2007
The multi-dimensional Black–Scholes equation is solved numerically for a European call basket opt... more The multi-dimensional Black–Scholes equation is solved numerically for a European call basket option using a priori–a posteriori error estimates. The equation is discretized by a finite difference method on a Cartesian grid. The grid is adjusted dynamically in space and time to satisfy a bound on the global error. The discretization errors in each time step are estimated and weighted by the solution of the adjoint problem. Bounds on the local errors and the adjoint solution are obtained by the maximum principle for parabolic equations. Comparisons are made with Monte Carlo and quasi-Monte Carlo methods in one dimension, and the performance of the method is illustrated by examples in one, two, and three dimensions.
Journal of Scientific Computing, 2015
Bit Numerical Mathematics, Jan 4, 2004
A Krylov iterative method in combination with a semi-Toeplitz preconditioner to solve the lineari... more A Krylov iterative method in combination with a semi-Toeplitz preconditioner to solve the linearized Navier–Stokes equations is presented. A scalar model problem is analyzed showing that the method has very favorable qualities. Numerical experiments for the flow problem corroborate the theory.
International Journal of Computer Mathematics, 2015
Computers & Mathematics with Applications, 2015
ABSTRACT A numerical method is developed for the solution of the Black–Scholes equation avoiding ... more ABSTRACT A numerical method is developed for the solution of the Black–Scholes equation avoiding the oscillations that are common close to a discontinuity in the pay-off function. Part of the derivatives are evaluated explicitly and part of them are computed implicitly using operator splitting. The method is second order accurate in time and almost of second order in the asset price for smooth solutions and no system of nonlinear equations has to be solved. A flux limiter modifies the first derivative in the equation such that no oscillations occur in the solution in the numerical examples presented.
We have dened and analyzed a semi-Toeplitz preconditioner for timedependentand steady-state conve... more We have dened and analyzed a semi-Toeplitz preconditioner for timedependentand steady-state convection-diusion problems. The preconditionerexhibits very good theoretical convergence properties. The analysis is corroboratedby numerical experiments.1
In this paper we develop a high-order adaptive finite difference space-discretization for the Bla... more In this paper we develop a high-order adaptive finite difference space-discretization for the Black-Scholes (B-S) equation. The final condition is discontinuous in the first derivative yielding that the effec- tive rate of convergence is two, both for low-order and high-order stan- dard finite difference (FD) schemes. To obtain a sixth-order scheme we use an extra grid in a limited space-
ABSTRACT The discontinuous Galerkin method for time integration of the Black-Scholes partial diff... more ABSTRACT The discontinuous Galerkin method for time integration of the Black-Scholes partial differential equation for option pricing problems is studied and compared with more standard time-integrators. In space an adaptive finite difference discretization is employed. The results show that the dG method are in most cases at least comparable to standard time-integrators and in some cases superior to them. Together with adaptive spatial grids the suggested pricing method shows great qualities.
Mathematics and Computers in Simulation, 2010
Quaternary Science Reviews, Sep 1, 2016
arXiv (Cornell University), Aug 28, 2019
Applied Mathematical Finance, Mar 3, 2020
Mathematics and Computers in Simulation, 2020
Geoscientific Model Development, 2020
International Journal of Computer Mathematics, 2018
Journal of Computational Physics, 2017
Quantitative Finance, 2011
Computers & Mathematics With Applications - COMPUT MATH APPL, 2007
The multi-dimensional Black–Scholes equation is solved numerically for a European call basket opt... more The multi-dimensional Black–Scholes equation is solved numerically for a European call basket option using a priori–a posteriori error estimates. The equation is discretized by a finite difference method on a Cartesian grid. The grid is adjusted dynamically in space and time to satisfy a bound on the global error. The discretization errors in each time step are estimated and weighted by the solution of the adjoint problem. Bounds on the local errors and the adjoint solution are obtained by the maximum principle for parabolic equations. Comparisons are made with Monte Carlo and quasi-Monte Carlo methods in one dimension, and the performance of the method is illustrated by examples in one, two, and three dimensions.
Journal of Scientific Computing, 2015
Bit Numerical Mathematics, Jan 4, 2004
A Krylov iterative method in combination with a semi-Toeplitz preconditioner to solve the lineari... more A Krylov iterative method in combination with a semi-Toeplitz preconditioner to solve the linearized Navier–Stokes equations is presented. A scalar model problem is analyzed showing that the method has very favorable qualities. Numerical experiments for the flow problem corroborate the theory.
International Journal of Computer Mathematics, 2015
Computers & Mathematics with Applications, 2015
ABSTRACT A numerical method is developed for the solution of the Black–Scholes equation avoiding ... more ABSTRACT A numerical method is developed for the solution of the Black–Scholes equation avoiding the oscillations that are common close to a discontinuity in the pay-off function. Part of the derivatives are evaluated explicitly and part of them are computed implicitly using operator splitting. The method is second order accurate in time and almost of second order in the asset price for smooth solutions and no system of nonlinear equations has to be solved. A flux limiter modifies the first derivative in the equation such that no oscillations occur in the solution in the numerical examples presented.
We have dened and analyzed a semi-Toeplitz preconditioner for timedependentand steady-state conve... more We have dened and analyzed a semi-Toeplitz preconditioner for timedependentand steady-state convection-diusion problems. The preconditionerexhibits very good theoretical convergence properties. The analysis is corroboratedby numerical experiments.1
In this paper we develop a high-order adaptive finite difference space-discretization for the Bla... more In this paper we develop a high-order adaptive finite difference space-discretization for the Black-Scholes (B-S) equation. The final condition is discontinuous in the first derivative yielding that the effec- tive rate of convergence is two, both for low-order and high-order stan- dard finite difference (FD) schemes. To obtain a sixth-order scheme we use an extra grid in a limited space-
ABSTRACT The discontinuous Galerkin method for time integration of the Black-Scholes partial diff... more ABSTRACT The discontinuous Galerkin method for time integration of the Black-Scholes partial differential equation for option pricing problems is studied and compared with more standard time-integrators. In space an adaptive finite difference discretization is employed. The results show that the dG method are in most cases at least comparable to standard time-integrators and in some cases superior to them. Together with adaptive spatial grids the suggested pricing method shows great qualities.
Mathematics and Computers in Simulation, 2010