Search results for "Compact finite difference"

showing 3 items of 3 documents

High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation

2001

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.

DiscretizationMathematical analysisFinite differenceFinite difference coefficientBlack–Scholes modelStability (probability)Parabolic partial differential equationNonlinear systemOption pricing transaction costs parabolic equations compact finite difference discretizationsValuation of optionsScheme (mathematics)Applied mathematicsddc:004General Economics Econometrics and FinanceFinanceMathematicsSSRN Electronic Journal
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Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation

2004

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

Matrix difference equationFTCS schemeNumerical AnalysisPartial differential equationApplied MathematicsMathematical analysisCompact finite differenceNumerical solution of the convection–diffusion equationFinite difference coefficientCentral differencing schemeComputational MathematicsModeling and SimulationAnalysisCompact convergenceMathematicsESAIM: Mathematical Modelling and Numerical Analysis
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Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation

2004

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

Nonlinear systemDiscretizationDifferential equationConvergence (routing)Finite differenceCompact finite differenceApplied mathematicsBlack–Scholes modelViscosity solutionHigh-order compact finite differences numerical convergence viscosity solution financial derivativesMathematics
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